\begin{thebibliography}{1000}

\bibitem{ipm:Abhyankar1}
S.~S. Abhyankar, T.~L. Morin, and T.~B. Trafalis.
\newblock Efficient faces of polytope\,: {Interior} point algorithms,
  parameterization of algebraic varieties, and multiple objective optimization.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,:\,Proceedings of a Joint
  Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA,
  June/July 1988}, volume 114 of {\em Contemporary Mathematics}, pages
  319--341. American Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Adler1}
I.~Adler.
\newblock A primal--dual implementation of {Karmarkar's} algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA,
  USA}, Operations Research Center, University of California, Berkeley,
  CA\,94720, USA, November 1985.

\bibitem{ipm:Adler13}
I.~Adler.
\newblock Computational tests of the {Karmarkar} algorithm.
\newblock {Talk held at the SIAM Conference on Optimization in Houston, TX,
  USA}, Department of Industrial Engineering and Operations Research,
  University of California, Berkeley, CA~94720, USA, May 1987.

\bibitem{ipm:Adler12}
I.~Adler.
\newblock Implementation issues of path--following algorithms for linear
  programming.
\newblock {Talk held at the EURO/TIMS Joint International Conference on
  Operational Research in Paris, France}, Department of Industrial Engineering
  and Operations Research, University of California, Berkeley, CA~94720, USA,
  July 1988.

\bibitem{ipm:Adler18}
I.~Adler and F.~Alizadeh.
\newblock Primal--dual interior point algorithms for convex quadratically
  constrained and semidefinite optimization problems.
\newblock {RUTCOR Research Report} RRR~46--95, RUTCOR -- Rutgers Center for
  Operations Research, Hill Center for Mathematical Sciences, New Brunswick,
  NJ~08903, USA, 1995.

\bibitem{ipm:Adler15}
I.~Adler and P.~A. Beling.
\newblock Polynomial algorithms for {LP} over a subring of the algebraic
  integers with applications to {LP} with circulant matrices.
\newblock {\em Mathematical Programming}, 57:121--143, 1992.
\newblock Condensed version in\,: {\em 32nd Annual Symposium on Foundations of
  Computer Science (San Juan, 1991), pp.\,480--487, IEEE Computer Society
  Press, Los Alamitos, CA, USA, 1991}.

\bibitem{ipm:Adler17}
I.~Adler and P.~A. Beling.
\newblock Polynomial algorithms for linear programming over the algebraic
  numbers.
\newblock {\em Algorithmica}, 12:436--457, 1994.

\bibitem{ipm:Adler7}
I.~Adler, {M. de} Carvalho, M.~G.~C. Resende, and G.~Veiga.
\newblock Computational performance of variants of {Karmarkar's} algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St. Louis,
  USA}, Department of Industrial Engineering and Operations Research,
  University of California, Berkeley, CA~94720, USA, October 1987.

\bibitem{ipm:Adler8}
I.~Adler, {M. de} Carvalho, M.~G.~C. Resende, and G.~Veiga.
\newblock A {Monte--Carlo} study of variants of interior point algorithms.
\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, University of California, Berkeley, CA~94720, USA, 1987.

\bibitem{ipm:Adler6}
I.~Adler, N.~K. Karmarkar, M.~G.~C. Resende, and G.~Veiga.
\newblock Implementation of an interior point algorithm for linear programming.
\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, University of California, Berkeley, CA\,94720, USA,
  1986.

\bibitem{ipm:Adler9}
I.~Adler, N.~K. Karmarkar, M.~G.~C. Resende, and G.~Veiga.
\newblock Data structures and programming techniques for the implementation of
  {Karmarkar's} algorithm.
\newblock {\em ORSA Journal on Computing}, 1:84--106, 1989.

\bibitem{ipm:Adler10}
I.~Adler, N.~K. Karmarkar, M.~G.~C. Resende, and G.~Veiga.
\newblock An implementation of {Karmarkar's} algorithm for linear programming.
\newblock {\em Mathematical Programming}, 44:297--335, 1989.
\newblock (Errata in {\em Mathematical Programming}, 50:415, 1991).

\bibitem{ipm:Adler5}
I.~Adler, N.~K. Karmarkar, and G.~Veiga.
\newblock Implementing an interior point algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
  FL, USA}, Department of Industrial Engineering and Operations Research,
  University of California, Berkeley, CA\,94720, USA, October 1986.

\bibitem{ipm:Adler14}
I.~Adler and R.~D.~C. Monteiro.
\newblock Limiting behavior of the affine scaling continuous trajectories for
  linear programming problems.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 189--211. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Adler11}
I.~Adler and R.~D.~C. Monteiro.
\newblock An interior point algorithm applied to a class of convex separable
  programming problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Industrial Engineering and Operations
  Research, University of California, Berkeley, CA~94720, USA, May 1991.

\bibitem{ipm:Adler2}
I.~Adler and R.~D.~C. Monteiro.
\newblock Limiting behavior of the affine scaling continuous trajectories for
  linear programming problems.
\newblock {\em Mathematical Programming}, 50:29--51, 1991.

\bibitem{ipm:Adler3}
I.~Adler and R.~D.~C. Monteiro.
\newblock A geometric view of parametric linear programming.
\newblock {\em Algorithmica}, 8:161--176, 1992.

\bibitem{ipm:Adler16}
I.~Adler and R.~Shamir.
\newblock A randomized scheme for speeding up algorithms for linear and convex
  programming with high constraints--to--variables ratio.
\newblock {\em Mathematical Programming}, 61:39--53, 1993.

\bibitem{ipm:Adler4}
I.~Adler and G.~Veiga.
\newblock On implementing interior point methods for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
  CA, USA}, Department of Industrial Engineering and Operations Research,
  University of California, Berkeley, CA\,94720, USA, April 1986.

\bibitem{ipm:Akguel2}
M.~Akg{\"{u}}l.
\newblock On the exact solution of a system of linear homogeneous equations via
  a projective algorithm.
\newblock {\em Arabian Journal for Science and Engineering}, 15(4):753--754,
  1990.

\bibitem{ipm:Akguel1}
M.~Akg{\"{u}}l.
\newblock A short proof of {Karmarkar's} main result.
\newblock {\em Do{\u{g}}a T{\"{u}}rk Matematik Dergisi (Turkish Journal of
  Mathematics, Ankara)}, 14:48--55, 1990.

\bibitem{ipm:Akrotirianakis1}
I.~Akrotirianakis and B.~Rustem.
\newblock A globally convergent interior point algorithm for general
  non--linear programming problems.
\newblock {Technical Report} 97--14, Department of Computing, Imperial College
  of Science, Technology and Medicine, 180~Queen's Gate, London\,SW7\,2BZ,
  United Kingdom, November 1997.

\bibitem{ipm:AlSultan2}
K.~S. {Al--Sultan}.
\newblock {\em Nearest point problems\,: {Theory} and algorithms}.
\newblock PhD thesis, University of Michigan, Ann Arbor, Michigan, USA, 1990.

\bibitem{ipm:AlSultan1}
K.~S. {Al--Sultan}.
\newblock A {Newton} based radius reduction algorithm for nearest point
  problems in pos cones.
\newblock {\em ORSA Journal on Computing}, 6:282--289, 1994.

\bibitem{ipm:Alfakih1}
A.~Y. Alfakih, A.~Khandani, and H.~Wolkowicz.
\newblock An interior--point algorithm for the {Euclidean} distance matrix
  completion problem.
\newblock {Research Report} CORR~97--9, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario, Canada, 1997.

\bibitem{ipm:Alizadeh4}
F.~Alizadeh.
\newblock {\em Combinatorial optimization with interior point methods and
  semi--definite matrices}.
\newblock PhD thesis, University of Minnesota, Minneapolis, Minnesota, USA,
  1991.

\bibitem{ipm:Alizadeh1}
F.~Alizadeh.
\newblock A sublinear--time randomized parallel algorithm for the maximum
  clique problem in perfect graphs.
\newblock {\em Proceedings of the Second ACM--SIAM Symposium on Discrete
  Algorithms}, pages 188--194, 1991.

\bibitem{ipm:Alizadeh3}
F.~Alizadeh.
\newblock Combinatorial optimization with semi--definite matrices.
\newblock In E.~Balas, G.~Cornu{\'e}jols, and R.~Kannan, editors, {\em
  Proceedings of the Second Integer Programming and Combinatorial Optimization
  (IPCO) Conference}, pages 385--405. Carnegie--Mellon University, Pittsburg,
  PA, USA, 1992.

\bibitem{ipm:Alizadeh2}
F.~Alizadeh.
\newblock Optimization over the positive semi-definite cone\,:
  {Interior--point} methods and combinatorial applications.
\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
  Computing}, pages 1--25. North Holland, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:Alizadeh5}
F.~Alizadeh.
\newblock Interior point methods in semidefinite programming with applications
  to combinatorial optimization.
\newblock {\em SIAM Journal on Optimization}, 5:13--51, 1995.

\bibitem{ipm:Alizadeh9}
F.~Alizadeh, J.-P.~A. Haeberly, M.~V. Nayakkankuppam, and M.~L. Overton.
\newblock {SDPpack} user's guide, version 0.8beta.
\newblock {Technical Report} 734, Department of Computer Science, New York
  University, New York, NY, USA, March 1997.

\bibitem{ipm:Alizadeh11}
F.~Alizadeh, J.-P.~A. Haeberly, M.~V. Nayakkankuppam, M.~L. Overton, and
  S.~Schmieta.
\newblock {SDPpack} user's guide, version 0.9beta.
\newblock {Technical Report} 737, Department of Computer Science, New York
  University, New York, NY, USA, 1997.

\bibitem{ipm:Alizadeh8}
F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
\newblock A new primal--dual interior--point method for semidefinite
  programming.
\newblock In J.~G. Lewis, editor, {\em Applied Linear Algebra (Proceedings of
  the 5th SIAM Conference, held in Snowbird, UT, USA, June 1994)}, pages
  113--117. SIAM Publications, Philadelphia, PA, USA, 1994.

\bibitem{ipm:Alizadeh6}
F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
\newblock Complementarity and nondegeneracy in semidefinite programming.
\newblock {RUTCOR Research Report}, RUTCOR -- Rutgers Center for Operations
  Research, Hill Center for Mathematical Sciences, New Brunswick, NJ~08903,
  USA, March 1995.

\bibitem{ipm:Alizadeh7}
F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
\newblock Primal--dual interior--point methods for semidefinite programming.
\newblock {RUTCOR Research Report}, RUTCOR -- Rutgers Center for Operations
  Research, Hill Center for Mathematical Sciences, New Brunswick, NJ~08903,
  USA, 1995.
\newblock Also published as\,: Technical Report, Courant Institute of
  Mathematical Sciences, New York University, New York, 1995.

\bibitem{ipm:Alizadeh10}
F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
\newblock Primal--dual interior--point methods for semidefinite programming\,:
  {Convergence} rates, stability and numerical results.
\newblock {\em SIAM Journal on Optimization}, 8:746--768, 1998.

\bibitem{ipm:Alizadeh12}
F.~Alizadeh and S.~Schmieta.
\newblock Optimization with semidefinite, quadratic and linear constraints.
\newblock {RUTCOR Research Report} RRR\,23--97, RUTCOR -- Rutgers Center for
  Operations Research, Hill Center for Mathematical Sciences, New Brunswick,
  NJ~08903, USA, November 1997.

\bibitem{ipm:Altman4}
A.~Altman.
\newblock An application of an interior point method for problems with
  uncertainty.
\newblock In A.~Bachem, U.~Derigs, M.~J{\"u}nger, and R.~Schrader, editors,
  {\em Operations Research~'93}, pages 5--7. Physica Verlag (A Springer--Verlag
  Company), Heidelberg, Germany, 1994.

\bibitem{ipm:Altman8}
A.~Altman.
\newblock The interior point method for nondifferentiable optimization.
\newblock {\em Journal of Computer and Systems Sciences International},
  33(6):12--21, 1995.

\bibitem{ipm:Altman5}
A.~Altman.
\newblock {\em QHOPDM} -- {A} higher order primal--dual method for large scale
  convex quadratic programming.
\newblock {\em European Journal of Operational Research}, 87:200--202, 1995.

\bibitem{ipm:Altman9}
A.~Altman.
\newblock Higher order primal--dual interior point method for separable convex
  quadratic optimization.
\newblock {\em Control and Cybernetics (Poland)}, 25:761--772, 1996.

\bibitem{ipm:Altman6}
A.~Altman, M.~Amann, G.~Klaassen, A.~Ruszczynski, and W.~Sch{\"o}pp.
\newblock Cost--effective sulphur emission reduction under uncertainty.
\newblock {\em European Journal of Operational Research}, 90:395--412, 1996.

\bibitem{ipm:Altman2}
A.~Altman and J.~Gondzio.
\newblock {\em HOPDM} -- {A} higher order primal--dual method for large scale
  linear programming.
\newblock {Program Manual}, Systems Research Institute, Polish Academy of
  Sciences, Newelska6, PL--01--447~Warshaw, Poland, July 1992.
\newblock See also Altman and Gondzio \cite{ipm:Altman3}.

\bibitem{ipm:Altman1}
A.~Altman and J.~Gondzio.
\newblock An efficient implementation of a higher order primal--dual interior
  point method for large sparse linear programs.
\newblock {\em Archives of Control Sciences}, 2:23--40, 1993.

\bibitem{ipm:Altman3}
A.~Altman and J.~Gondzio.
\newblock {\em HOPDM} -- {A} higher order primal--dual method for large scale
  linear programming.
\newblock {\em European Journal of Operational Research}, 66:159--160, 1993.
\newblock See also Altman and Gondzio \cite{ipm:Altman2}, and Gondzio
  \cite{ipm:Gondzio9}.

\bibitem{ipm:Altman10}
A.~Altman and J.~Gondzio.
\newblock Regularized symmetric indefinite systems in interior point methods
  for linear and quadratic optimization.
\newblock {Logilab Technical Report} 98.6, Section of Management Studies,
  University of Geneva, 102 Bd. Carl Vogt, CH--1211 Geneva 4, Switzerland,
  March 1998.

\bibitem{ipm:Altman7}
A.~Altman and K.~C. Kiwiel.
\newblock A note on some analytic center cutting plane methods for convex
  feasibility and minimization problems.
\newblock {\em Computational Optimization and Applications}, 5:175--180, 1996.

\bibitem{ipm:Amaya1}
J.~Amaya.
\newblock Numerical experiments with the symmetric affine scaling algorithm on
  degenerate linear programming problems.
\newblock {\em Optimization}, 27:51--62, 1993.

\bibitem{ipm:Amaya2}
J.~Amaya.
\newblock On the symmetric affine scaling algorithm for linear programming.
\newblock {\em Optimization}, 32:147--158, 1995.

\bibitem{ipm:Andersen7}
E.~D. Andersen.
\newblock Finding all linearly dependent rows in large--scale linear
  programming.
\newblock {\em Optimization Methods and Software}, 6:219--2227, 1995.

\bibitem{ipm:Andersen19}
E.~D. Andersen.
\newblock Implementation of interior point methods for large scale linear
  programming.
\newblock {Technical Report} 96--1, Department of Management, School of
  Business and Admininstration, Odense Uinversity, Odense, Denmark, 1996.

\bibitem{ipm:Andersen21}
E.~D. Andersen.
\newblock On exploiting problem structure in a basis identification procedure
  for linear programming.
\newblock {Technical Report} 96--6, Department of Management, School of
  Business and Admininstration, Odense Uinversity, Odense, Denmark, 1996.

\bibitem{ipm:Andersen16}
E.~D. Andersen.
\newblock {\em Solution of linear and convex optimization problems with
  interior--point methods}.
\newblock PhD thesis, Department of Mathematics and Computer Science, Odense
  University,, DK--5320~Odense~M, Denmark, January 1996.

\bibitem{ipm:Andersen26}
E.~D. Andersen.
\newblock The homogeneous self--dual methods for linear programming.
\newblock In C.~A. Floudas and P.~M. Pardalos, editors, {\em Encyclopaedia of
  Optimization}. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.

\bibitem{ipm:Andersen9}
E.~D. Andersen and K.~D. Andersen.
\newblock Presolving in linear programming.
\newblock {\em Mathematical Programming}, 71:221--245, 1995.

\bibitem{ipm:Andersen18}
E.~D. Andersen and K.~D. Andersen.
\newblock {The APOS LP solver}.
\newblock {Technical Report}, Center of Operations Research and Econometrics,
  Universite Catholique de Louvain, B--1348~Louvain--la--Neuve, Belgium, 1995.

\bibitem{ipm:Andersen20}
E.~D. Andersen and K.~D. Andersen.
\newblock {The APOS linear programming solver\,: An} implementation of the
  homogeneous algorithm.
\newblock {CORE Discussion Paper} 9337, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, 1997.

\bibitem{ipm:Andersen24}
E.~D. Andersen and K.~D. Andersen.
\newblock A parallel interior--point algorithm for linear programming on a
  shared memory machine.
\newblock {CORE Discussion Paper} 9808, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, 1998.

\bibitem{ipm:Andersen25}
E.~D. Andersen and A.~Damgaard.
\newblock Utility based option pricing with proportional transaction costs and
  diversification problems\,: {An} interior point optimization approach.
\newblock {Technical Report}, Department of Management, School of Business and
  Admininstration, Odense University, Odense, Denmark, 1997.

\bibitem{ipm:Anderson15}
E.~D. Andersen, J.~Gondzio, C.~M{\'e}sz{\'a}ros, and X.~Xu.
\newblock Implementation of interior point methods for large scale linear
  programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 189--252. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Andersen6}
E.~D. Andersen and Y.~Ye.
\newblock Combining interior--point algorithms and pivoting for linear
  programming.
\newblock {\em Management Science}, 42:1719--1731, 1996.

\bibitem{ipm:Andersen23}
E.~D. Andersen and Y.~Ye.
\newblock On a homogeneous algorithm for a monotone complementarity problem
  with nonlinear equality constraints.
\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
  Variational Problems\,: State--of--the--Art (Baltimore 1995)}, pages 1--11.
  SIAM Publications, Philadelphia, PA, USA, 1997.

\bibitem{ipm:Andersen22}
E.~D. Andersen and Y.~Ye.
\newblock A computational study of the homogeneous algorithm for large-- scale
  convex optimization.
\newblock {\em Computational Optimization and Applications}, 10:243--269, 1998.

\bibitem{ipm:Andersen13}
E.~D. Andersen and Y.~Ye.
\newblock On a homogeneous algorithm for the monotone complementarity problem.
\newblock {\em Mathematical Programming}, 84:375--399, 1999.

\bibitem{ipm:Andersen5}
J.~A. Andersen.
\newblock {\em Iterative methods for the solution of linear programs}.
\newblock PhD thesis, Department of Mathematics and Statistics, Brunel
  University, Uxbridge, Middlesex~UB8\,3PH, United Kingdom, 1992.

\bibitem{ipm:Andersen4}
J.~A. Andersen, R.~Levkovitz, and G.~Mitra.
\newblock Adapting the interior point method for the solution of linear
  programs on high performance computers.
\newblock In O.~Balci, R.~Sharda, and S.~A. Zenios, editors, {\em Operations
  Research and Computer Science\,: New Developments in Their Interfaces}, pages
  73--86. Pergamon Press, Oxford, United Kingdom, 1992.

\bibitem{ipm:Andersen1}
J.~A. Andersen, R.~Levkovitz, G.~Mitra, and M.~Tamiz.
\newblock Adopting interior search algorithms for the solution of {LP}s for
  serial, coarse grain parallel and massively parallel computers.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Department of Mathematics and Statistics, Brunel University,
  Uxbridge, Middlesex~UB8~3PH, United Kingdom, January 1990.

\bibitem{ipm:Andersen2}
J.~A. Andersen and G.~Mitra.
\newblock Solving the {Newton} iteration step of the interior point method on
  massively parallel ({SIMD}) computer.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Department of Mathematics and Statistics, Brunel University, Uxbridge,
  Middlesex~UB8~3PH, United Kingdom, January 1991.

\bibitem{ipm:Andersen3}
K.~D. Andersen.
\newblock An infeasible dual affine scaling method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Bulletin}, 22:19--27, 1993.

\bibitem{ipm:Andersen10}
K.~D. Andersen.
\newblock A large scaling implementation of the dual affine scaling algorithm.
\newblock Preprint, Department of Mathematics and Computer Science, Odense
  University, DK--5320~Odense~M, Denmark, 1993.
\newblock To appear in {\em Mathematical Programming Society Committee on
  Algorithms (COAL) Bulletin}.

\bibitem{ipm:Andersen17}
K.~D. Andersen.
\newblock An efficient {Newton} barrier method for minimizing a sum of
  {Euclidean} norms.
\newblock {\em SIAM Journal on Optimization}, 6:74--95, 1996.

\bibitem{ipm:Andersen11}
K.~D. Andersen.
\newblock A modified {Schur} complement for handling dense columns in interior
  point methods for linear programming.
\newblock {\em ACM Transactions on Mathematical Software}, 22:348--356, 1996.

\bibitem{ipm:Andersen8}
K.~D. Andersen and E.~Christiansen.
\newblock Limit analysis with the dual affine scaling algorithm.
\newblock {\em Journal of Computational and Applied Mathematics}, 59:233--243,
  1995.

\bibitem{ipm:Andersen27}
K.~D. Andersen, E.~Christiansen, A.~R. Conn, and M.~L. Overton.
\newblock An efficient primal--dual interior--point method for minimizing a sum
  of {Euclidean} norms.
\newblock {CORE Discussion Paper}, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, August 1998.

\bibitem{ipm:Andersen12}
K.~D. Andersen and E.~D. Christiansen.
\newblock A {Newton} barrier method for minimizing a sum of {Euclidean} norms
  subject to linear equality constraints.
\newblock Preprint 95--07, Department of Mathematics and Computer Science,
  Odense University, DK--5320~Odense~M, Denmark, February 1995.

\bibitem{ipm:Andersen14}
K.~D. Andersen and E.~D. Christiansen.
\newblock A symmetric primal--dual {Newton} method for minimizing a sum of
  norms.
\newblock Preprint, Department of Mathematics and Computer Science, Odense
  University, DK--5320~Odense~M, Denmark, 1995.

\bibitem{ipm:Andrusenko1}
S.~K. Andrusenko, E.~A. Nurminskii, and P.~I. Stetsyuk.
\newblock Numerical experiments in a new class of algorithms in linear
  programming.
\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
  (Moscow)}, 27:349--356, 1987.
\newblock Translated in\,: {\em USSR Computational Mathematics and Mathematical
  Physics}, 27(2):18--22, 1987.

\bibitem{ipm:Angier1}
N.~Angier.
\newblock Folding the perfect corner.
\newblock {\em Time Magazin}, 124:55, December 3, 1984.

\bibitem{ipm:Anitescu2}
M.~Anitescu, G.~Lesaja, and F.~Potra.
\newblock Equivalence between different formulations of the linear
  complementarity problem.
\newblock {Reports on Computational Mathematics}~71, Department of Mathematics,
  University of Iowa, Iowa City, IA~52242, USA, June 1995.

\bibitem{ipm:Anitescu1}
M.~Anitescu, G.~Lesaja, and F.~Potra.
\newblock An infeasible--interior--point predictor--corrector algorithm for the
  {$P_{*}$}--geometric {LCP}.
\newblock {\em Applied Mathematics and Optimization}, 36:203--228, 1997.

\bibitem{ipm:Anstreicher1}
K.~M. Anstreicher.
\newblock Analysis of a modified {Karmarkar} algorithm for linear programming.
\newblock {Technical Report} B\#84, Yale School of Management, Yale University,
  New Haven, CT~06520, USA, August 1985.

\bibitem{ipm:Anstreicher2}
K.~M. Anstreicher.
\newblock Analysis of {Karmarkar's} algorithm for fractional linear
  programming.
\newblock {Technical Report}, Yale School of Management, Yale University, New
  Haven, CT~06520, USA, November 1985.

\bibitem{ipm:Anstreicher3}
K.~M. Anstreicher.
\newblock A monotonic projective algorithm for fractional linear programming.
\newblock {\em Algorithmica}, 1(4):483--498, 1986.

\bibitem{ipm:Anstreicher4}
K.~M. Anstreicher.
\newblock A strenghtened acceptance criterion for approximate projections in
  {Karmarkar's} algorithm.
\newblock {\em Operations Research Letters}, 5:211--214, 1986.

\bibitem{ipm:Anstreicher5}
K.~M. Anstreicher.
\newblock On the complexity of the projective algorithm for standard form
  linear programming.
\newblock {Technical Report} B\#104, Yale School of Management, Yale
  University, New Haven, CT~06520, USA, 1987.

\bibitem{ipm:Anstreicher7}
K.~M. Anstreicher.
\newblock Linear programming and the {Newton} barrier flow.
\newblock {\em Mathematical Programming}, 41:367--373, 1988.

\bibitem{ipm:Anstreicher18}
K.~M. Anstreicher.
\newblock A combined phase\,{I}\,--\,phase\,{II} projective algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 43:209--223, 1989.

\bibitem{ipm:Anstreicher10}
K.~M. Anstreicher.
\newblock Progress in interior point algorithms since 1984.
\newblock {\em SIAM News}, 22:12--14, March 1989.

\bibitem{ipm:Anstreicher22}
K.~M. Anstreicher.
\newblock Recent developments in algorithms for linear programming.
\newblock {Talk held at the Third SIAM Conference on Optimization in Boston,
  MA, USA}, Yale School of Management, Yale University, New Haven, CT~06520,
  USA, April 1989.

\bibitem{ipm:Anstreicher9}
K.~M. Anstreicher.
\newblock The worst--case step in {Karmarkar's} algorithm.
\newblock {\em Mathematics of Operations Research}, 14:294--302, 1989.

\bibitem{ipm:Anstreicher6}
K.~M. Anstreicher.
\newblock Dual ellipsoids and degeneracy in the projective algorithm for linear
  programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 141--149. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Anstreicher12}
K.~M. Anstreicher.
\newblock A standard form variant and safeguarded linesearch for the modified
  {Karmarkar} algorithm.
\newblock {\em Mathematical Programming}, 47:337--351, 1990.

\bibitem{ipm:Anstreicher23}
K.~M. Anstreicher.
\newblock Advances in interior point methods for linear programming.
\newblock {Tutorial held at the ORSA/TIMS Joint National Meeting in Anaheim,
  CA, USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, November 1991.

\bibitem{ipm:Anstreicher11}
K.~M. Anstreicher.
\newblock A combined phase\,{I}\,--\,phase\,{II} scaled potential algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 52:429--439, 1991.

\bibitem{ipm:Anstreicher17}
K.~M. Anstreicher.
\newblock On monotonicity in the scaled potential algorithm for linear
  programming.
\newblock {\em Linear Algebra and Its Applications}, 152:223--232, 1991.

\bibitem{ipm:Anstreicher8}
K.~M. Anstreicher.
\newblock On the performance of {Karmarkar's} algorithm over a sequence of
  iterations.
\newblock {\em SIAM Journal on Optimization}, 1(1):22--29, 1991.

\bibitem{ipm:Anstreicher25}
K.~M. Anstreicher.
\newblock Efficient centering for linear programming interior point methods.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, January 1992.

\bibitem{ipm:Anstreicher20}
K.~M. Anstreicher.
\newblock On interior algorithms for linear programming with no regularity
  assumptions.
\newblock {\em Operations Research Letters}, 11:209--212, 1992.

\bibitem{ipm:Anstreicher16}
K.~M. Anstreicher.
\newblock Strict monotonicity and improved complexity in the standard form
  projective algorithm for linear programming.
\newblock {\em Mathematical Programming}, 62:517--535, 1993.

\bibitem{ipm:Anstreicher31}
K.~M. Anstreicher.
\newblock Large step volumetric potential reduction algorithms for linear
  programming.
\newblock {\em Annals of Operations Research}, 62:521--538, 1996.

\bibitem{ipm:Anstreicher19}
K.~M. Anstreicher.
\newblock On long step path following and {SUMT} for linear and quadratic
  programming.
\newblock {\em SIAM Journal on Optimization}, 6:33--46, 1996.

\bibitem{ipm:Anstreicher37}
K.~M. Anstreicher.
\newblock Potential reduction algorithms.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 125--158. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Anstreicher38}
K.~M. Anstreicher.
\newblock Ellipsoidal approximations of convex sets based on the volumetric
  barrier.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, March 1997.

\bibitem{ipm:Anstreicher36}
K.~M. Anstreicher.
\newblock {\em {Interior Point Methods in Theory and Practice}}, volume~76 of
  {\em Mathematical Programming}.
\newblock North Holland, Amsterdam, The Netherlands, 1997.
\newblock (Special issue).

\bibitem{ipm:Anstreicher32}
K.~M. Anstreicher.
\newblock On {Vaidya's} volumetric cutting plane method for convex programming.
\newblock {\em Mathematics of Operations Research}, 22:63--89, 1997.

\bibitem{ipm:Anstreicher33}
K.~M. Anstreicher.
\newblock Volumetric path following algorithms for linear programming.
\newblock {\em Mathematical Programming}, 76:245--263, 1997.

\bibitem{ipm:Anstreicher42}
K.~M. Anstreicher.
\newblock On the equivalence of convex programming bounds for {Boolean}
  quadratic programming.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, May 1998.

\bibitem{ipm:Anstreicher44}
K.~M. Anstreicher.
\newblock The volumetric barrier for convex quadratic constraints.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, October 1998.

\bibitem{ipm:Anstreicher40}
K.~M. Anstreicher.
\newblock The volumetric barrier for semidefinite programming.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, January 1998.

\bibitem{ipm:Anstreicher39}
K.~M. Anstreicher.
\newblock Towards a practical volumetric cutting plane method for convex
  programming.
\newblock {\em SIAM Journal on Optimization}, 9:190--206, 1999.

\bibitem{ipm:Anstreicher21}
K.~M. Anstreicher and R.~A. Bosch.
\newblock On partial updating in a potential reduction linear programming
  algorithm of {Kojima, Mizuno and Yoshise}.
\newblock {Technical Report}, Yale School of Management, Yale University, New
  Haven, CT~06520, USA, 1991.
\newblock Same as Bosch and Anstreicher \cite{ipm:Bosch2}.

\bibitem{ipm:Anstreicher13}
K.~M. Anstreicher and R.~A. Bosch.
\newblock Long steps in a ${O(n^{3}L)}$ algorithm for linear programming.
\newblock {\em Mathematical Programming}, 54:251--265, 1992.

\bibitem{ipm:Anstreicher30}
K.~M. Anstreicher and R.~A. Bosch.
\newblock A new infinity--norm path following algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:236--246, 1995.

\bibitem{ipm:Anstreicher35}
K.~M. Anstreicher and M.~Fampa.
\newblock A long--step path following algorithm for semidefinite programming
  problems.
\newblock In P.~M. Pardalos and M.~Wolkowicz, editors, {\em Topics in
  Semidefinite and Interior--Point Methods}, volume~18 of {\em Fields Institute
  Communications Series}, pages 181--196. American Mathematical Society (AMS),
  Providence, RI, USA, 1998.

\bibitem{ipm:Freund34}
K.~M. Anstreicher and R.~M. Freund.
\newblock Following a ''balanced'' trajectory from an infeasible point to an
  optimal linear programming solution with a polynomial--time algorithm.
\newblock {\em Mathematics of Operations Research}, 21:839--859, 1996.

\bibitem{ipm:Anstreicher34}
K.~M. Anstreicher and R.~M. Freund.
\newblock {\em {Interior Point Methods in Mathematical Programming}}, volume~62
  of {\em Annals of Operations Research}.
\newblock Baltzer Science Publishing Company, Basel, Switzerland, 1996.
\newblock Special issue.

\bibitem{ipm:Anstreicher15}
K.~M. Anstreicher, {D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A long step barrier method for convex quadratic programming.
\newblock {\em Algorithmica}, 10:365--382, 1993.

\bibitem{ipm:Anstreicher24}
K.~M. Anstreicher and J.~Ji.
\newblock More on dual ellipsoids and degeneracy in interior algorithms for
  linear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, May 1992.

\bibitem{ipm:Anstreicher27}
K.~M. Anstreicher, J.~Ji, F.~A. Potra, and Y.~Ye.
\newblock Probabilistic analysis of an infeasible primal--dual algorithm for
  linear programming.
\newblock {Reports on Computational Mathematics}~27, Department of Mathematics,
  University of Iowa, Iowa City, IA~52242, USA, July 1992.

\bibitem{ipm:Anstreicher28}
K.~M. Anstreicher, J.~Ji, F.~A. Potra, and Y.~Ye.
\newblock Average performance of a self--dual interior--point algorithm for
  linear programming.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 1--15. World Scientific Publishing Co., London, United
  Kingdom, 1993.

\bibitem{ipm:Anstreicher26}
K.~M. Anstreicher, J.~Ji, and Y.~Ye.
\newblock Average performance of an ellipsoid termination criterion for linear
  programming interior point algorithms.
\newblock {Technical Report} 92--01, Department of Management Science,
  University of Iowa, Iowa City, IA~52242, USA, February 1992.

\bibitem{ipm:Anstreicher29}
K.~M. Anstreicher and J.-Ph. Vial.
\newblock On the convergence of an infeasible primal--dual interior--point
  method for convex programming.
\newblock {\em Optimization Methods and Software}, 3:273--283, 1994.

\bibitem{ipm:Anstreicher14}
K.~M. Anstreicher and P.~Watteyne.
\newblock A family of search directions for {Karmarkar's} algorithm.
\newblock {\em Operations Research}, 41:759--767, 1993.

\bibitem{ipm:Anstreicher41}
K.~M. Anstreicher and H.~Wolkowicz.
\newblock On {Lagrangian} relaxation of quadratic matrix constraints.
\newblock {Research Report} CORR 98--24, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario~N2L\,3G1, Canada,
  1998.

\bibitem{ipm:Arbel1}
A.~Arbel.
\newblock {\em {Exploring Interior Point Linear Programming\,: Algorithms and
  Software}}.
\newblock Foundations of Computing Series. MIT Press, Cambridge, MA~02142, USA,
  1993.

\bibitem{ipm:Arbel4}
A.~Arbel.
\newblock Generating interior search directions for multiobjective linear
  programming using approximate gradients and efficient anchoring points.
\newblock {\em Optimization}, 28:149--164, 1993.

\bibitem{ipm:Arbel2}
A.~Arbel.
\newblock An interior multiobjective linear programming algorithm.
\newblock {\em Computers and Operations Research}, 20(7):723--735, 1993.

\bibitem{ipm:Arbel12}
A.~Arbel.
\newblock Large--scale optimization methods applied to the cutting stock
  problem of irregular shapes.
\newblock {\em International Journal of Production Research}, 31:483--500,
  1993.

\bibitem{ipm:Arbel7}
A.~Arbel.
\newblock Using sequential generation of anchoring points in an interior
  multi--objective primal--dual linear programming algorithm.
\newblock {\em Archives of Control Sciences}, 2:5--21, 1993.

\bibitem{ipm:Arbel11}
A.~Arbel.
\newblock A weighted--gradient approach to multi--objective linear programming
  problems using the analytical hierarchy process.
\newblock {\em Mathematical Computations and Modelling}, 17(4--5):27--39, 1993.

\bibitem{ipm:Arbel3}
A.~Arbel.
\newblock Anchoring points and cones of opportunities in interior
  multiobjective linear programming.
\newblock {\em Journal of the Operational Research Society}, 45(1):83--96,
  1994.

\bibitem{ipm:Arbel9}
A.~Arbel.
\newblock Interior--point methods for multiobjective linear programming
  problems.
\newblock In G.~H.~Tzeng et~al., editor, {\em Multiple Criteria Decision
  Making, Proceedings of the 10th International Conference ''Expand and Enrich
  the Domain of Thinking and Application'', held at Taipei, Taiwan, July 1992},
  pages 27--36. Springer Verlag, Berlin, Germany, 1994.

\bibitem{ipm:Arbel5}
A.~Arbel.
\newblock An interior multiobjective primal--dual linear programming algorithm
  using approximated gradients and sequential generation of anchor points.
\newblock {\em Optimization}, 30:137--150, 1994.

\bibitem{ipm:Arbel8}
A.~Arbel.
\newblock A multiobjective interior primal--dual linear programming algorithm.
\newblock {\em Computers and Operations Research}, 21:433--445, 1994.

\bibitem{ipm:Arbel6}
A.~Arbel.
\newblock Using efficient anchoring points for generating search directions in
  interior multi--objective linear programming.
\newblock {\em Journal of the Operational Research Society}, 45:330--334, 1994.

\bibitem{ipm:Arbel13}
A.~Arbel.
\newblock An interior multiple objective primal--dual linear programming
  algorithm using efficient anchoring points.
\newblock {\em Journal of the Operational Research Society}, 46:1121--1132,
  1995.

\bibitem{ipm:Arbel17}
A.~Arbel.
\newblock An interior multiobjective primal--dual linear programming algorithm
  based on approximated gradients and efficient anchoring points.
\newblock {\em Computers and Operations Research}, 24:353--365, 1997.

\bibitem{ipm:Arbel16}
A.~Arbel and P.~Korhonen.
\newblock Using aspiration levels in an interactive interior multiobjective
  linear programming algorithm.
\newblock {\em European Journal of the Operational Research}, 89:193--201,
  1996.

\bibitem{ipm:Arbel18}
A.~Arbel and P.~Korhonen.
\newblock Using aspiration levels in an interior primal--dual multiobjective
  linear programming algorithm.
\newblock {\em Journal of Multi--Criteria Decisions and Analysis}, 5:61--71,
  1996.

\bibitem{ipm:Arbel15}
A.~Arbel and S.~S. Oren.
\newblock Generating interior search directions for multiobjective linear
  programming.
\newblock {\em Journal of Multi--Criteria Decisions and Analysis}, 2:73--86,
  1993.

\bibitem{ipm:Arbel10}
A.~Arbel and S.~S. Oren.
\newblock A modification of {Karmarkar's} algorithm for multiple objective
  linear programming.
\newblock In G.~H. Tzeng, editor, {\em Multiple Criteria Decision Making,
  Proceedings of the 10th International Conference ''Expand and Enrich the
  Domain of Thinking and Application'', held at Taipei, Taiwan, July 1992},
  pages 37--46. Springer Verlag, Berlin, Germany, 1994.

\bibitem{ipm:Arbel14}
A.~Arbel and S.~S. Oren.
\newblock Using approximate gradients in developing an interactive interior
  primal--dual multiobjective linear programming algorithm.
\newblock {\em European Journal of the Operational Research}, 89:202--211,
  1996.

\bibitem{ipm:Arbel19}
A.~Arbel and P.Korhonen.
\newblock An interior multiobjective linear programming algorithm using
  aspirations.
\newblock In G.~Fandel and T.~Gal, editors, {\em Multiple Criteria Decision
  Making, Proceedings of the Conference held at Hagen, Germany, 1995}, volume
  448 of {\em Lecture Notes in Economics and Mathematical Systems}, pages
  245--254. Springer Verlag, Berlin, Germany, 1997.

\bibitem{ipm:ArgaezRamos1}
M.~{Arg{\'a}ez Ramos}.
\newblock {\em Exact and inexact {Newton} linesearch interior--point algorithms
  for nonlinear programming problems}.
\newblock PhD thesis, Department of Computational and Applied Mathematics, Rice
  University, Houston, TX~77251, USA, 1997.
\newblock Available as\,: Technical Report TR97--13.

\bibitem{ipm:Armacost1}
A.~Armacost and S.~Mehrotra.
\newblock A computational comparison of the network simplex method with the
  dual affine scaling method.
\newblock {\em Journal of the Operational Research Society of India
  (Opsearch)}, 28(1):18--35, 1991.

\bibitem{ipm:Armand1}
P.~Armand, J.~C. Gilbert, and S.~Jan-J{\'e}gou.
\newblock A feasible {BFGS} interior point algorithm for solving strongly
  convex minimization problems.
\newblock {Research Report} 3500, Institute National de Recherche en
  Informatique et Automatique (INRIA), F--78153~Roquencourt, France, October
  1998.

\bibitem{ipm:Aronson1}
J.~Aronson, R.~Barr, R.~Helgason, J.~Kennington, A.~Loh, and H.~Zaki.
\newblock The projective transformation algorithm by {Karmarkar}\,: {A}
  computational experiment with assignment problems.
\newblock {Technical Report} 85--OR--3, Department of Operations Research,
  Southern Methodist University, Dallas, TX~75275, USA, August 1985.

\bibitem{ipm:Aronson2}
J.~Aronson, R.~Barr, R.~Helgason, J.~Kennington, A.~Loh, and H.~Zaki.
\newblock A specialization of {Karmarkar's} algorithm to solve network
  problems.
\newblock {Technical Report}, Department of Operations Research, Southern
  Methodist University, Dallas, TX~75275, USA, 1985.

\bibitem{ipm:Astfalk1}
G.~Astfalk, I.~J. Lustig, R.~E. Marsten, and D.~Shanno.
\newblock The interior--point method for linear programming.
\newblock {\em IEEE Software}, 9(4):61--68, 1992.

\bibitem{ipm:At1}
{The {AT~\&~T KORBX} Linear Programming System, AT~\&~T Bell Laboratories,
  Holmdel, NJ~07733, USA}, 1988.
\newblock Introduced at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA, October 1988.

\bibitem{ipm:Atkinson6}
D.~S. Atkinson.
\newblock {\em Scaling and interior--point methods in optimization}.
\newblock PhD thesis, Coordinated Science Laboratory, College of Engineering,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1992.

\bibitem{ipm:Atkinson3}
D.~S. Atkinson and P.~M. Vaidya.
\newblock An analytic center based cutting plane algorithm for convex
  programming.
\newblock {Technical Report}, College of Commerce and Business Administration,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, June
  1992.

\bibitem{ipm:Atkinson2}
D.~S. Atkinson and P.~M. Vaidya.
\newblock A cutting plane algorithm that uses analytic centers.
\newblock {Working Paper}, College of Commerce and Business Administration,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1992.

\bibitem{ipm:Atkinson5}
D.~S. Atkinson and P.~M. Vaidya.
\newblock Minimizing weighted self--concordant logarithmic barrier functions by
  scaling.
\newblock {Preprint}, Department of Mathematics, University of Illinois at
  Urbana--Champaign, Urbana, IL~61820, USA, 1992.

\bibitem{ipm:Atkinson1}
D.~S. Atkinson and P.~M. Vaidya.
\newblock A scaling technique for finding the weighted analytic center of a
  polytope.
\newblock {\em Mathematical Programming}, 57:163--192, 1992.

\bibitem{ipm:Atkinson4}
D.~S. Atkinson and P.~M. Vaidya.
\newblock A cutting plane algorithm for convex programming that uses analytic
  centers.
\newblock {\em Mathematical Programming}, 69:1--43, 1995.

\bibitem{ipm:Asic4}
M.~D. A\u{s}i{\'c} and V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}.
\newblock An interior semi--infinite programming method.
\newblock {\em Journal of Optimization Theory and Applications}, 59:369--390,
  1988.

\bibitem{ipm:Asic8}
M.~D. A\u{s}i{\'c} and V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}.
\newblock Ill--conditionedness and interior--point methods.
\newblock {Technical Report}, Laboratory for Operations Research, Faculty of
  Organizational Sciences, University of Belgrade, Jove Ilica~154,
  YU--11040~Belgrade, Yugoslavia, February 1998.

\bibitem{ipm:Asic6}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Karmarkar algoritam\,: {Analiza} numericke stabilnosti i neke
  modifikacije.
\newblock {\em Proceedings of the 12th Yugoslav Symposium on Operations
  Research (Herceg--Novi, Yugoslavia, October 1985)}, pages 33--41, 1985.
\newblock (In Yugoslav).

\bibitem{ipm:Asic7}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Asimptotsko ponasanje {Karmarkarove} metode.
\newblock {\em Proceedings of the 13th Yugoslav Symposium on Operations
  Research (Herceg--Novi, Yugoslavia, October 1986)}, pages 81--88, 1986.
\newblock (In Yugoslav).

\bibitem{ipm:Asic3}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Asymptotic behavior and numerical stability of {Karmarkar's} method
  for linear programming.
\newblock {Technical Report}, University of Belgrade, Belgrade, Yugoslavia,
  1986.

\bibitem{ipm:Asic1}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Behavior of {Karmarkar's} method on degenerate problems.
\newblock {Technical Report}, Department of Mathematics, Michigan State
  University, East Lansing, MI~48824, USA, 1988.

\bibitem{ipm:Asic2}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Asymptotic behavior of {Karmarkar's} method for linear programming.
\newblock {\em Mathematical Programming}, 46:173--190, 1990.

\bibitem{ipm:Asic5}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock A note on limiting behavior of the projective and the affine
  rescaling algorithms.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 151--157. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Auslender1}
A.~Auslender and M.~Haddou.
\newblock An interior--proximal method for convex linearly constrained problems
  and its extension to variational inequalities.
\newblock {\em Mathematical Programming}, 71:77--100, 1995.

\bibitem{ipm:Babrovnikova1}
E.~Babrovnikova and S.~Vavasis.
\newblock Accurate solution of weighted least squares by iterative methods.
\newblock {Preprint} ANL/MSC--P644--0297, Mathematics and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, February 1997.

\bibitem{ipm:Bach1}
R.~Bach.
\newblock {{\"U}ber die Effizienz eines polynomialen Verfahrens zur L{\"o}sung
  von linearen Optimierungsproblemen. (About the efficiency of a polynomial
  method for solving linear programming problems)}.
\newblock Master's thesis, {Fachbereich Wirtschaftswissenschaften und
  Operations Research, FernUniversit{\"a}t Hagen}, P. O. Box 940, D--5800
  Hagen, Germany, December 1990.
\newblock (In German).

\bibitem{ipm:Bachem1}
A.~Bachem and M.~Strietzel.
\newblock {Eine parallele Implementierung des Karmarkar--Verfahrens (A parallel
  implementation of Karmarkar's method)}.
\newblock {Technical Report} 92--121, Department of Mathematics, University of
  Cologne, Cologne, Germany, 1992.
\newblock (In German).

\bibitem{ipm:Bachem2}
A.~Bachem and M.~Strietzel.
\newblock {Einbettung der parallelen Grundsoftware CARO in die primale--duale
  Barrierfunktionsmethode (Imbedding of the parallel basic software CARO into
  the primal--dual barrier function method)}.
\newblock {Technical Report} 93--129, Department of Mathematics, University of
  Cologne, Cologne, Germany, 1993.
\newblock (In German).

\bibitem{ipm:Bagchi1}
A.~Bagchi and B.~Kalantari.
\newblock A method for computing approximate solution of the trust region
  problem with application to projective methods for quadratic programming.
\newblock {Working Paper}, Department of Computer Science, Rutgers University,
  New Brunswick, NJ~08903, USA, 1988.

\bibitem{ipm:Bahn1}
O.~Bahn, J.-L. Goffin, J.-Ph. Vial, and O.~Du Merle.
\newblock Implementation and behavior of an interior point cutting plane
  algorithm for convex programming\,: {An} application to geometric
  programming.
\newblock {Working Paper}, University of Geneva, Geneva, Switzerland, 1991.
\newblock See also Bahn et al.\,\cite{ipm:Bahn3}.

\bibitem{ipm:Bahn3}
O.~Bahn, J.-L. Goffin, J.-Ph. Vial, and O.~Du Merle.
\newblock Experimental behavior of an interior point cutting plane algorithm
  for convex programming\,:\,{An} application to geometric programming.
\newblock {\em Discrete Applied Mathematics}, 49:3--23, 1994.
\newblock See also Bahn et al.\,\cite{ipm:Bahn1}.

\bibitem{ipm:Bahn2}
O.~Bahn, O.~Du Merle, J.-L. Goffin, and J.-Ph. Vial.
\newblock A cutting plane method from analytic centers for stochastic
  programming.
\newblock {\em Mathematical Programming}, 69:45--73, 1995.

\bibitem{ipm:Bai1}
E.~Bai, Y.~Ye, and R.~Tempo.
\newblock Bounded error parameter estimation\,: {A} sequential analytic center
  approach.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1997.

\bibitem{ipm:Balakrishnan1}
V.~Balakrishnan, E.~Feron, S.~Boyd, and L.~{El Ghaoui}.
\newblock Computing bounds for the structured singular value via interior point
  algorithm.
\newblock {\em Proceedings of the American Control Conference (Chicago, IL,
  USA, June 1992)}, 3:2195--2196, 1994.

\bibitem{ipm:Ballintijn1}
C.~Ballintijn.
\newblock Implementation aspects and performance results of the dual--affine
  algorithm.
\newblock {Talk held at the 14th Conference on the Mathematics of Operations
  Research in Dalfsen, The Netherlands}, Koninklijke Shell Laboratorium
  Amsterdam (KSLA), Amsterdam, The Netherlands, January 1990.
\newblock See Marsten et al.\,\cite{ipm:Marsten5}.

\bibitem{ipm:Barle1}
J.~Barle and J.~Grad.
\newblock The implementation of {Karmarkar's} algorithm using electronic
  spreadsheet.
\newblock {Talk held at the DGOR--Jahrestagung in Berlin, Germany}, Ekonomska
  Fakulteta Borisa Kidrica, University of Ljubljana, YU--61109~Ljubljana,
  Yugoslavia, September 1988.

\bibitem{ipm:Barle2}
J.~Barle and J.~Grad.
\newblock The implementations of interior point methods for solving {LP on PC}.
\newblock {\em Operations Research Proceedings 1992}, pages 26--33, 1992.

\bibitem{ipm:Barnes2}
E.~R. Barnes.
\newblock A sparse matrix version of {Karmarkar's} algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences,
  IBM~T.~J.~Watson Research Center, P.\,O.\,Box 218, Yorktown Heights,
  NY~10598, USA, 1986.

\bibitem{ipm:Barnes1}
E.~R. Barnes.
\newblock A variation on {Karmarkar's} algorithm for solving linear programming
  problems.
\newblock {\em Mathematical Programming}, 36:174--182, 1986.

\bibitem{ipm:Barnes3}
E.~R. Barnes.
\newblock A polynomial--time version of the affine scaling algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
  USA}, Department of Mathematical Sciences, IBM~T.~J.~Watson Research Center,
  P.~O.~Box~218, Yorktown Heights, NY~10598, USA, October 1987.

\bibitem{ipm:Barnes5}
E.~R. Barnes.
\newblock Phase--{I} procedures for interior point problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Department of Mathematical Sciences, IBM~T.~J.~Watson Research Center,
  P.~O.~Box~218, Yorktown Heights, NY~10598, USA, April 1988.

\bibitem{ipm:Barnes4}
E.~R. Barnes.
\newblock The role of centering in interior point methods.
\newblock {Technical Report}, Department of Mathematical Sciences,
  IBM~T.~J.~Watson Research Center, P.~O.~Box~218, Yorktown Heights, NY~10598,
  USA, 1988.

\bibitem{ipm:Barnes7}
E.~R. Barnes.
\newblock Computing centers and minimum covering ellipsoids for polytopes.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, School of Industrial and Systems Engineering, Georgia Institute of
  Technology, Atlanta, GA~30322--0205, USA, October 1989.

\bibitem{ipm:Barnes6}
E.~R. Barnes.
\newblock Numerical techniques for interior point methods.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Institute of Technology, Atlanta, GA~30322--0205, USA, 1989.

\bibitem{ipm:Barnes13}
E.~R. Barnes.
\newblock Some results concerning convergence of the affine scaling algorithm.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 131--139. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Barnes14}
E.~R. Barnes.
\newblock Minimum containing ellipsoids and regular polyhedra.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:2--6, August 1991.

\bibitem{ipm:Barnes9}
E.~R. Barnes, S.~Chopra, and D.~J. Jensen.
\newblock Polynomial--time convergence of the affine scaling algorithm with
  centering.
\newblock {Talk held at the Conference on Progress in Mathematical Programming,
  Asimolar Conference Center, Pacific Grove, CA, USA}, Department of
  Mathematical Sciences, IBM~T.~J.~Watson Research Center, P.~O.~Box~218,
  Yorktown Heights, NY~10598, USA, March 1987.

\bibitem{ipm:Barnes10}
E.~R. Barnes, S.~Chopra, and D.~J. Jensen.
\newblock The affine scaling method with centering.
\newblock {Technical Report}, Department of Mathematical Sciences,
  IBM~T.~J.~Watson Research Center, P.~O.~Box~218, Yorktown Heights, NY~10598,
  USA, 1988.

\bibitem{ipm:Barnes11}
E.~R. Barnes, S.~Chopra, and D.~J. Jensen.
\newblock A polynomial--time version of the affine--scaling algorithm.
\newblock {Working Paper Series} 88--101, Graduate School of Business and
  Administration, New York University, New York, NY~10006, USA, 1988.

\bibitem{ipm:Barnes8}
E.~R. Barnes and D.~J. Jensen.
\newblock Affine--scaling algorithms for linear programming with centering
  steps.
\newblock {Technical Report}, Department of Mathematical Sciences,
  IBM~T.~J.~Watson Research Center, P.~O.~Box~218, Yorktown Heights, NY~10598,
  USA, 1987.

\bibitem{ipm:Barnes12}
E.~R. Barnes and A.~Moretti.
\newblock On the convergence of the affine scaling algorithm.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Institute of Technology, Atlanta, GA~30332--0205, USA, 1991.

\bibitem{ipm:Barutt1}
J.~F. Barutt, J.~A. Ludvijsen, and E.~M. Olsen.
\newblock Using the interior point method for solving large scale crew
  scheduling problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Northwest Airlines F--7140, MSP International Airport, St.~Paul,
  MN~55111, USA, May 1990.

\bibitem{ipm:Batterman1}
A.~Batterman and M.~Heinkenschloss.
\newblock Preconditioners for {Karush--Kuhn--Tucker} matrices arising in the
  optimal control of distributed systems.
\newblock {Technical Report} TR~96--34, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1996.

\bibitem{ipm:Bayer4}
D.~A. Bayer, N.~K. Karmarkar, and J.~C. Lagarias.
\newblock Methods and apparatus for optimization system operational parameters.
\newblock U.~S.~Patent No.~4.744.027, 1988.
\newblock AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA.

\bibitem{ipm:Bayer2}
D.~A. Bayer and J.~C. Lagarias.
\newblock The nonlinear geometry of linear programming, {Part\,I\,: Affine} and
  projective scaling trajectories.
\newblock {\em Transactions of the American Mathematical Society},
  314(2):499--526, 1989.

\bibitem{ipm:Bayer3}
D.~A. Bayer and J.~C. Lagarias.
\newblock The nonlinear geometry of linear programming, {Part\,II\,: Legendre}
  transform coordinates.
\newblock {\em Transactions of the American Mathematical Society},
  314(2):527--581, 1989.

\bibitem{ipm:Bayer1}
D.~A. Bayer and J.~C. Lagarias.
\newblock Karmarkar's linear programming algorithm and {N}ewton's method.
\newblock {\em Mathematical Programming}, 50:291--330, 1991.

\bibitem{ipm:Bazaraa1}
M.~S. Bazaraa, J.~J. Jarvis, and H.~F. Sherali.
\newblock {\em Linear Programming and Network Flows}, chapter 8.4\,:
  {Karmarkar's} projective algorithm, pages 380--394, chapter 8.5~: {A}nalysis
  of {Karmarkar's} algorithm, pages 394--418.
\newblock John Wiley \& Sons, New York, second edition, 1990.

\bibitem{ipm:Beasley1}
J.~E. Beasley.
\newblock {\em {Advances in Linear and Integer Programming}}, volume~4 of {\em
  Oxford Lecture Series in Mathematics and its Applications}.
\newblock Oxford Science Publications, Oxford University Press, Oxford, Great
  Britain, 1996.

\bibitem{ipm:Beck1}
C.~Beck.
\newblock Computational issues in solving {LMIs} (linear matrix inequalities).
\newblock {\em Proceedings of the 30th IEEE Conference on Decision and Control
  (Brighton, United Kingdom, December 1991)}, 2:1259--1260, 1991.

\bibitem{ipm:Beisel2}
E.~P. Beisel.
\newblock {Affin--transformierende global konvergente Innere--Punkte--Verfahren
  der linearen Optimierung mit langen Schrittweiten (Affine--scaling globally
  convergent long step interior--point methods for linear programming)}.
\newblock {Habilitationthesis}, Fachbereich Mathematik, Bergische
  Universit{\"a}t-- Gesamthochschule Wuppertal, Gauss--str. 20,
  D--42097~Wuppertal, Germany, 1996.
\newblock (In German).

\bibitem{ipm:Beisel1}
E.~P. Beisel and M.~Mendel.
\newblock {\em {Optimierungsmethoden des Operations Research, Band\,1
  (Optimization Methods of Operations Research, Vol.\,1)}}, chapter 11\,: {Die
  Projektionsmethode von Karmarkar~(The projection method of Karmarkar)}, pages
  169--187.
\newblock Vieweg Verlag, Braunschweig, Germany, 1987.
\newblock (In German).

\bibitem{ipm:Belegundu1}
A.~D. Belegundu, L.~Berke, and S.~N. Patnaik.
\newblock An optimization algorithm based on the method of feasible directions.
\newblock {\em Structural Optimization}, 9:83--88, 1995.

\bibitem{ipm:Bellavia1}
S.~Bellavia.
\newblock Inexact interior--point method.
\newblock {\em Journal of Optimization Theory and Applications}, 96:109--121,
  1998.

\bibitem{ipm:BenDaya3}
M.~{Ben--Daya}.
\newblock Line search techniques for the logarithmic barrier function in
  quadratic programming.
\newblock {\em Journal of the Operational Research Society}, 46:322--328, 1995.

\bibitem{ipm:BenDaya1}
M.~{Ben--Daya} and C.~M. Shetty.
\newblock Polynomial barrier function algorithm for linear programming.
\newblock {Technical Report} J~88--4, School of Industrial and Systems
  Engineering, Georgia Institute of Technology, Atlanta, GA~30322--0205, USA,
  1988.

\bibitem{ipm:BenDaya2}
M.~{Ben--Daya} and C.~M. Shetty.
\newblock Polynomial barrier function algorithm for convex quadratic
  programming.
\newblock {\em Arabian Journal for Science and Engineering}, 15(4):657--670,
  1990.

\bibitem{ipm:BenTal1}
A.~{Ben--Tal} and A.~S. Nemirovsky.
\newblock Interior point polynomial time method for truss topology design.
\newblock {Technical Report} 3/92, Optimization Laboratory, Faculty of
  Industrial Engineering and Management at Technion, Technion City,
  Haifa~32000, Israel, June 1992.

\bibitem{ipm:BenTal3}
A.~{Ben--Tal} and A.~S. Nemirovsky.
\newblock An interior point algorithm for truss topology design.
\newblock In M.~P. Bendsoe and C.~A. Soares, editors, {\em Topology Design of
  Structures}, pages 55--69. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1993.

\bibitem{ipm:BenTal2}
A.~{Ben--Tal} and A.~S. Nemirovsky.
\newblock Potential reduction polynomial time method for truss topology design.
\newblock {\em SIAM Journal on Optimization}, 4:596--612, 1994.

\bibitem{ipm:BenTal7}
A.~{Ben--Tal} and A.~S. Nemirovsky.
\newblock Structural design via semidefinite programming.
\newblock {Working Paper}, Optimization Laboratory, Faculty of Industrial
  Engineering and Management Technion -- Israel Institute of Technology,
  Technion City, Haifa~32000, Israel, August 1997.

\bibitem{ipm:BenTal8}
A.~{Ben--Tal} and A.~S. Nemirovsky.
\newblock On polyhedral approximations of the second--order cone.
\newblock {Research Report} 3/98, Optimization Laboratory, Faculty of
  Industrial Engineering and Management Technion -- Israel Institute of
  Technology, Technion City, Haifa~32000, Israel, 1998.

\bibitem{ipm:BenTal9}
A.~{Ben--Tal} and A.~S. Nemirovsky.
\newblock On the quality of {SDP} approximations of uncertain {SDP} programs.
\newblock {Research Report} 4/98, Optimization Laboratory, Faculty of
  Industrial Engineering and Management Technion -- Israel Institute of
  Technology, Technion City, Haifa~32000, Israel, 1998.

\bibitem{ipm:BenTal5}
A.~{Ben--Tal} and G.~Roth.
\newblock A truncated log barrier algorithm for large--scale convex programming
  and minimax problems\,: {Implementation} and computational results.
\newblock {\em Optimization Methods and Software}, 6:283--312, 1996.

\bibitem{ipm:BenTal6}
A.~{Ben--Tal} and M.~Zibulevsky.
\newblock Penalty/barrier multipliers methods\,: {A} new class of augmented
  {Lagrangian} algorithms for large--scale convex programming problems.
\newblock {Research Report} 4/93, Optimization Laboratory, Faculty of
  Industrial Engineering and Management, Technion, Israel Institute of
  Technology, Haifa~32000, Israel, 1993.

\bibitem{ipm:BenTal4}
A.~{Ben--Tal}, M.~Zibulevsky, and I.~Yusefovich.
\newblock Penalty/barriers multipliers methods for minimax and constrained
  smooth convex programs.
\newblock {Research Report} 9/92, Optimization Laboratory, Faculty of
  Industrial Engineering and Management, Technion, Israel Institute of
  Technology, Haifa, Israel, 1992.

\bibitem{ipm:Benchakroun1}
A.~Benchakroun, J.~P. Dussault, and A.~Mansouri.
\newblock Local convergence analysis of the method of centers.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Universite de Sherbrooke, Sherbrooke, Canada, May 1992.

\bibitem{ipm:Benchakroun2}
A.~Benchakroun, J.~P. Dussault, and A.~Mansouri.
\newblock Un algorithme de points interieurs pour un probleme de programmation
  non--lineaire.
\newblock {\em Information Systems and Operational Research (INFORS)},
  35:239--248, 1997.

\bibitem{ipm:Benjamin1}
J.~Benjamin and M.~Dialsy.
\newblock Some applications of the primal--dual interior point algorithm using
  {GAUSS} programming language.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Economics Department, North Carolina A\,\&\,T State University,
  Greensboro, NC~27411, USA, October 1990.

\bibitem{ipm:Benson1}
S.~Benson, Y.~Ye, and X.~Zhang.
\newblock Solving large--scale sparse semidefinite programs for combinatorial
  optimization.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, August 1997.

\bibitem{ipm:Benson2}
S.~Benson, Y.~Ye, and X.~Zhang.
\newblock Mixed linear and semidefinite programming for combinatorial and
  quadratic optimization.
\newblock {Working Paper}, Applied Mathematics and Computer SCiences,
  University of Iowa, Iowa City, IA~52242, USA, February 1998.

\bibitem{ipm:Bentham1}
{H. van} Bentham, A.~Hipolito, B.~Jansen, C.~Roos, T.~Terlaky, and J.~Warners.
\newblock Radio link frequency assignment project\,: {Potential} reduction
  methods.
\newblock {Technical Annex} T--2.3.2, Faculty of Technical Mathematics and
  Informatics, Delft University of Technology, Delft, The Netherlands, 1995.

\bibitem{ipm:Berger1}
A.~J. Berger, J.~M. Mulvey, and A.~Ruszczynski.
\newblock An extension of the {DQA} algorithm to convex stochastic programs.
\newblock {\em SIAM Journal on Optimization}, 4:735--753, 1994.

\bibitem{ipm:Berke1}
L.~Berke, N.~Khot, R.~Polyak, and R.~Schneur.
\newblock Application of the {Newton} modified barrier method in structural
  optimizations.
\newblock {\em Proceedings of the 33rd American Institute of Aeronautics and
  Astronautics (AIAA) Conference}, 1992.

\bibitem{ipm:Berkelaar3}
A.~Berkelaar, C.~Roos, and T.~Terlaky.
\newblock The optimal set and optimal partition approach for linear and
  quadratic programming.
\newblock In T.~Gal and H.~J. Greenberg, editors, {\em Advances in Sensitivity
  Analysis and Parametric Programming}, volume~6 of {\em International Series
  in Operations Research and Management Science}, pages 6.1--6.44. Kluwer
  Academic Press, Dordrecht, The Netherlands, 1997.

\bibitem{ipm:Berkelaar2}
A.~B. Berkelaar, B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Optimal basis and optimal tripartition identification algorithms for
  quadratic programming and linear complementarity problems -- from an interior
  solution to a basis solution and vice versa.
\newblock {Technical Report}, Faculty of Technical Mathematics and Informatics,
  TU Delft, NL--2600~GA~Delft, The Netherlands, March 1996.

\bibitem{ipm:Berkelaar1}
A.~B. Berkelaar, B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Sensitivity analysis for degenerate quadratic programming.
\newblock {Technical Report}, Faculty of Technical Mathematics and Informatics,
  TU Delft, NL--2600~GA~Delft, The Netherlands, February 1996.

\bibitem{ipm:Bertsekas1}
D.~P. Bertsekas.
\newblock Projected {N}ewton methods for optimization problems with simple
  constraints.
\newblock {\em SIAM Journal on Control and Optimization}, 20:221--246, 1982.

\bibitem{ipm:Bertsimas1}
D.~Bertsimas and X.~Luo.
\newblock On the worst case complexity of potential reduction algorithms for
  linear programming.
\newblock {\em Mathematical Programming}, 77:321--333, 1997.

\bibitem{ipm:Bertsimas3}
D.~Bertsimas and J.~B. Orlin.
\newblock A technique for speeding up the solution of the {Lagrangian} dual.
\newblock {\em Mathematical Programming}, 63:23--45, 1994.

\bibitem{ipm:Bertsimas2}
D.~Bertsimas and J.~Tsitsiklis.
\newblock {\em Introduction to Linear Optimization}.
\newblock Athena Scientific, 1997.

\bibitem{ipm:Betke1}
U.~Betke and P.~Gritzmann.
\newblock Projection algorithms for linear programming.
\newblock {\em European Journal of Operational Research}, 60:287--295, 1992.

\bibitem{ipm:Biegler1}
L.~Biegler, J.~Nocedal, C.~Schmitt, and D.~Ternet.
\newblock Numerical experience with a reduced {Hessian} method for large scale
  optimization.
\newblock {Technical Report} OTC\,97/06, Optimization Technology Center,
  Northwestern University, Evanston, IL~60208--3119, USA, July 1997.

\bibitem{ipm:Billups1}
S.~C. Billups and S.~C. Ferris.
\newblock Convergence of infeasible interior--point algorithms from arbitrary
  starting points.
\newblock {\em SIAM Journal on Optimization}, 6:316--325, 1996.

\bibitem{ipm:Birge3}
J.~R. Birge, R.~M. Freund, and R.~J. Vanderbei.
\newblock Prior reduced fill--in in solving equations in interior point
  algorithm.
\newblock {Working Paper} OR~3186--90--MS, Sloan School of Management,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, 1990.
\newblock See also Birge, Freund and Vanderbei \cite{ipm:Birge7}.

\bibitem{ipm:Birge7}
J.~R. Birge, R.~M. Freund, and R.~J. Vanderbei.
\newblock Prior reduced fill--in in solving equations in interior point
  algorithms.
\newblock {\em Operations Research Letters}, 11:195--198, 1992.

\bibitem{ipm:Birge5}
J.~R. Birge and D.~Holmes.
\newblock Using interior point methods for stochastic linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Industrial and Operations Engineering, University of
  Michigan, Ann Arbor, MI~48104, USA, November 1991.
\newblock See Birge and Holmes \cite{ipm:Birge6}.

\bibitem{ipm:Birge6}
J.~R. Birge and D.~F. Holmes.
\newblock Efficient solution of two stage stochastic linear programs using
  interior point methods.
\newblock {\em Computational Optimization and Applications}, 1:245--276, 1992.

\bibitem{ipm:Birge1}
J.~R. Birge and L.~Qi.
\newblock Solving stochastic linear programs via a variant of {Karmarkar's}
  algorithm.
\newblock {Technical Report} 85--12, Department of Industrial and Operations
  Engineering, University of Michigan, Ann Arbor, MI~48103, USA, 1985.

\bibitem{ipm:Birge2}
J.~R. Birge and L.~Qi.
\newblock Computing block--angular {Karmarkar} projections with applications to
  stochastic programming.
\newblock {\em Management Science}, 34:1472--1479, 1988.

\bibitem{ipm:Birge4}
J.~R. Birge and C.~Rosa.
\newblock A simplified proof of the general convergence of affine scaling.
\newblock {Technical Report} 91--7, Department of Industrial and Operations
  Engineering, University of Michigan, Ann Arbor, MI~48104, USA, 1991.

\bibitem{ipm:Birge8}
J.~R. Birge and H.~Tang.
\newblock Computing {Karmarkar's} projections quickly by using matrix
  factorization.
\newblock {\em Applied Mathematics, A Journal of the Chinese Universities
  (Series B)}, 11:227--248, 1996.

\bibitem{ipm:Bisseling1}
R.~H. Bisseling, T.~M. Doup, and {L. D. J. C.} Loyens.
\newblock A parallel interior point algorithm for linear programming on a
  network of transputers.
\newblock {\em Annals of Operations Research}, 43:51--86, 1993.

\bibitem{ipm:Bixby1}
R.~E. Bixby, J.~W. Gregory, I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Very large--scale linear programming\,: {A} case study in combining
  interior point and simplex methods.
\newblock {\em Operations Research}, 40:885--897, 1992.

\bibitem{ipm:Bixby2}
R.~E. Bixby and M.~J. Saltzman.
\newblock Recovering an optimal {LP} basis from an interior point solution.
\newblock {\em Operations Research Letters}, 15:169--178, 1994.

\bibitem{ipm:Blair1}
C.~E. Blair.
\newblock The iterative step in the linear programming algorithm of {N.
  Karmarkar}.
\newblock {\em Algorithmica}, 1(4):537--539, 1986.

\bibitem{ipm:Blair2}
C.~E. Blair.
\newblock {Karmarkar's} algorithm and the simplex algorithm.
\newblock {Technical Report}, College of Commerce and Business Administration,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1989.

\bibitem{ipm:Blanchon1}
G.~Blanchon, J.-C. Dodu, A.~Renaud, and M.~Bouhtou.
\newblock Implementation of a primal--dual interior--point method applied to
  the planning of reactive power compensation devices.
\newblock {\em Proceedings of the Twelfth Power Systems Computation
  Conference}, 2:827--836, 1996.

\bibitem{ipm:Bloch1}
A.~M. Bloch.
\newblock Steepest descent, linear programming, and {Hamiltonian} flows.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 77--88. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Blum1}
L.~Blum.
\newblock Towards an asymptotic analysis of {Karmarkar's} algorithm.
\newblock {\em Information Processing Letters}, 23:189--194, 1986.

\bibitem{ipm:Blum2}
L.~Blum.
\newblock A new simple homotopy algorithm for linear programming {I}.
\newblock {\em Journal of Complexity}, 4:124--136, 1988.

\bibitem{ipm:Boggs4}
P.~T. Boggs.
\newblock Comparing algorithms is not an easy task.
\newblock {\em SIAM News}, 19(1):7, 1986.

\bibitem{ipm:Boggs3}
P.~T. Boggs.
\newblock Higher--order methods for large linear and quadratic programming
  problems.
\newblock {Talk held at the Second International Conference on Industrial and
  Applied Mathematics (ICIAM~'91), Washington, DC, USA}, United States
  Department of Commerce, National Institute of Standards and Technology,
  Center for Applied Mathematics, Gaithersburg, MD~20899, USA, July 1991.

\bibitem{ipm:Boggs6}
P.~T. Boggs.
\newblock Interior point methods.
\newblock {Technical Report}, United States Department of Commerce, National
  Institute of Standards and Technology, Center for Applied Mathematics,
  Gaithersburg, MD~20899, USA, 1995.
\newblock To appear in {\em Encyclopedia of Operations Research}.

\bibitem{ipm:Boggs2}
P.~T. Boggs, P.~D. Domich, J.~R. Donaldson, and C.~Witzgall.
\newblock Algorithmic enhancements to the method of center for linear
  programming.
\newblock {\em ORSA Journal on Computing}, 1:159--171, 1989.

\bibitem{ipm:Boggs5}
P.~T. Boggs, P.~D. Domich, J.~E. Rogers, and C.~Witzgall.
\newblock An interior--point method for linear and quadratic programming
  problems.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:32--40, August 1991.

\bibitem{ipm:Boggs7}
P.~T. Boggs, P.~D. Domich, J.~E. Rogers, and C.~Witzgall.
\newblock An interior--point method for general large scale quadratic
  programming problems.
\newblock {\em Annals of Operations Research}, 62:419--437, 1996.

\bibitem{ipm:Boggs1}
P.~T. Boggs, P.~D. Domich, and C.~Witzgall.
\newblock On center trajectories for linear programming.
\newblock {Technical Report}, United States Department of Commerce, National
  Institute of Standards and Technology, Center for Applied Mathematics,
  Gaithersburg, MD~20899, USA, 1988.

\bibitem{ipm:Bonnans1}
J.~F. Bonnans and M.~Bouhtou.
\newblock An interior point affine algorithm for convex programming based on a
  potential function.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Institute National de Recherche en Informatique et Automatique
  (INRIA), F--78153~Roquencourt, France, May 1992.

\bibitem{ipm:Bonnans2}
J.~F. Bonnans and M.~Bouhtou.
\newblock The trust region affine interior point algorithm for convex and
  nonconvex quadratic programming.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  29:195--217, 1995.

\bibitem{ipm:Bonnans7}
J.~F. Bonnans, J.~C. Gilbert, C.~Lemar{\'e}chal, and C.~Sagastiz{\'a}bal.
\newblock {\em {Optimisation Num{\'e}rique\, : Aspects Th{\'e}oriques et
  Pratiques}}, volume 257 of {\em Math{\'e}matique \& Applications}, chapter
  {Part\,IV\,: Algorithmes de points int{\'e}rieurs pour l'optimisation
  lin{\'e}aire et quadratique (Interior point algorithms for linear and
  quadratic optimization)}, pages 203--310.
\newblock Springer Verlag, Paris, France, 1997.
\newblock (In French).

\bibitem{ipm:Bonnans3}
J.~F. Bonnans and C.~C. Gonzaga.
\newblock Convergence of interior--point algorithms for the monotone linear
  complementarity problem.
\newblock {\em Mathematics of Operations Research}, 21:1--25, 1996.

\bibitem{ipm:Bonnans4}
J.~F. Bonnans and C.~Pola.
\newblock A trust region interior point algorithm for linearly constrained
  optimization.
\newblock {\em SIAM Journal on Optimization}, 7:717--731, 1997.

\bibitem{ipm:Bonnans6}
J.~F. Bonnans and F.~A. Potra.
\newblock Infeasible path--following algorithms for linear complementarity
  problems.
\newblock {Reports on Computational Mathematics}~63, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, 1994.
\newblock To appear in {\em Mathematics of Operations Research}. See also Potra
  and Bonnans \cite{ipm:Potra12}.

\bibitem{ipm:Bonnans5}
J.~F. Bonnans and F.~A. Potra.
\newblock On the convergence of the iteration sequence of infeasible
  path--following algorithms for linear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 22:378--407, 1997.

\bibitem{ipm:Borchers2}
B.~Borchers.
\newblock {\em Improved branch and bound algorithms for integer programming}.
\newblock PhD thesis, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, June 1992.

\bibitem{ipm:Borchers3}
B.~Borchers.
\newblock {CSDP}\,: {A C} library for semidefinite programming.
\newblock {Technical Report}, Faculty of Mathematics, Institute of Mining and
  Technology, New Mexico Tech, Socorro, NM, USA, 1997.

\bibitem{ipm:Borchers5}
B.~Borchers.
\newblock {SDPLIB\,1.0}\,: {A} collection of semidefinite programming test
  problems.
\newblock {Technical Report}, Faculty of Mathematics, Institute of Mining and
  Technology, New Mexico Tech, Socorro, NM, USA, July 1998.

\bibitem{ipm:Borchers1}
B.~Borchers and J.~E. Mitchell.
\newblock Using an interior point method in a branch and bound algorithm for
  integer programming.
\newblock {RPI Mathematical Report} 195, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, 1991.
\newblock Revised July 1992.

\bibitem{ipm:Borchers4}
B.~Borchers and J.~E. Mitchell.
\newblock A computational comparison of branch and bound and outer
  approximation algorithms for $0--1$ mixed integer nonlinear programs.
\newblock {\em Computers and Operations Research}, 24:699--701, 1997.

\bibitem{ipm:Bosch3}
R.~A. Bosch.
\newblock On {Mizuno's} rank one updating algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 3:861--867, 1993.

\bibitem{ipm:Bosch4}
R.~A. Bosch.
\newblock A new proof of a partial updating theorem.
\newblock {Technical Report}, Department of Mathematics, Oberlin College,
  Oberlin, OH~44074, USA, 1995.

\bibitem{ipm:Bosch2}
R.~A. Bosch and K.~M. Anstreicher.
\newblock On partial updating in a potential reduction linear programming
  algorithm of {Kojima, Mizuno and Yoshise}.
\newblock {\em Algorithmica}, 9(1):184--197, 1993.
\newblock Same as Anstreicher and Bosch \cite{ipm:Anstreicher21}.

\bibitem{ipm:Bosch1}
R.~A. Bosch and K.~M. Anstreicher.
\newblock A partial updating algorithm for linear programs with many more
  variables than constraints.
\newblock {\em Optimization Methods and Software}, 4:243--257, 1995.

\bibitem{ipm:Bosch5}
R.~A. Bosch and R.~V. Torenbeek.
\newblock A family of algorithms for approximating the smallest eigenvalue of a
  matrix with no complex eigenvalues.
\newblock {Technical Report}, Department of Mathematics, Oberlin College,
  Oberlin, OH~44074, USA, 1995.

\bibitem{ipm:Bouhtou1}
M.~Bouhtou.
\newblock {\em M{\'e}thodes de points int{\'e}rieurs pour l'optimisation des
  syst{\`e}mes de grande taille ({Interior point methods for large--scale
  optimization systems})}.
\newblock PhD thesis, Laboratoire de Analyse et Modelisation de Syst{\`e}mes
  pour l'Aide a la Decision (LAMSADE), Universit{\'e} de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1993.
\newblock (In French).

\bibitem{ipm:Boukari1}
D.~Boukari and A.~V. Fiacco.
\newblock Survey of penalty, exact penalty and multiplier methods from 1968 to
  1993.
\newblock {\em Optimization}, 30:301--334, 1995.

\bibitem{ipm:Box1}
M.~J. Box, D.~Davies, and W.~H. Swann.
\newblock {\em Nonlinear Optimization Technique}, volume~5 of {\em ICI
  Monograph of Mathematics and Statistics}.
\newblock Oliver and Boyd Ltd., London, United Kingdom, 1969.

\bibitem{ipm:Boyd1}
S.~Boyd and L.~{El Ghaoui}.
\newblock Methods of centers for minimizing generalized eigenvalues.
\newblock {\em Linear Algebra and Its Applications}, 188/189:63--111, 1993.

\bibitem{ipm:Boyd3}
S.~Boyd, L.~{El Ghaoui}, E.~Feron, and V.~Balakrishnan.
\newblock {\em Linear Matrix Inequalities in System and Control Theory},
  volume~15 of {\em SIAM Studies in Applied Mathematics}.
\newblock Society of Industrial and Applied Mathematics (SIAM), Philadelphia,
  PA~19101, USA, 1994.

\bibitem{ipm:Boyd4}
S.~Boyd and L.~Vandenberghe.
\newblock {CRCD} program\,: {Convex} optimization for engineering analysis and
  design.
\newblock {\em Proceedings of the 1995 American Control Conference}, Part
  2/6:1069--1071, 1995.

\bibitem{ipm:Boyd2}
S.~Boyd, L.~Vandenberghe, and M.~Grant.
\newblock Efficient convex optimization for engineering design.
\newblock {ISL--Report}, Department of Electrical Engineering, Information
  Systems Laboratory, Stanford University, Stanford, CA~94305, USA, 1994.
\newblock Submitted to {\em Automatica}.

\bibitem{ipm:Branch1}
M.~A. Branch, T.~F. Coleman, and Y.~Li.
\newblock A subspace, interior, and conjugate gradient method for large--scale
  bound--constrained minimization problems.
\newblock {Technical Report} TR~95--1525, Department of Computer Science,
  Cornell University, Ithaca, NY~14853, USA, 1995.

\bibitem{ipm:Bregman1}
L.~M. Bregman.
\newblock A polynomial--time simplex type method for solving linear systems of
  inequalities.
\newblock {\em Kibernetika (Kiev)}, 26(1):84--87, 1990.
\newblock Translated in\,: {\em Cybernetics (USA)}, 26(1):106--110, 1990.

\bibitem{ipm:Breitfeld3}
M.~G. Breitfeld and D.~F. Shanno.
\newblock A globally convergent penalty--barrier algorithm for nonlinear
  programming and its computational performance.
\newblock {Research Report} RRR~12--94, RUTCOR\,--\,Rutgers Center for
  Operations Research, Rutgers University, Busch Campus, New Brunswick,
  NJ~08903, USA, 1994.
\newblock Submitted to {\em Mathematical Programming}.

\bibitem{ipm:Breitfeld1}
M.~G. Breitfeld and D.~F. Shanno.
\newblock Preliminary computational experience with modified log--barrier
  functions for large--scale nonlinear programming.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 45--67. Kluwer
  Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Breitfeld2}
M.~G. Breitfeld and D.~F. Shanno.
\newblock Computational experience with penalty--barrier methods for nonlinear
  programming.
\newblock {\em Annals of Operations Research}, 62:439--463, 1996.

\bibitem{ipm:Brophy1}
J.~F. Brophy and P.~W. Smith.
\newblock Prototyping {Karmarkar's} algorithm using {MATH/PROTRAN}.
\newblock {\em International Mathematical and Statistical Libraries (IMSL)
  Directions}, 5:2--3, 1988.

\bibitem{ipm:Brown2}
G.~G. Brown, R.~D. McBride, and K.~R. Wood.
\newblock Computational methods in the projective linear programming algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA,
  USA}, Department of Operations Research, Naval Postgraduate School, Monterey,
  CA~93943, USA, November 1985.

\bibitem{ipm:Brown1}
G.~W. Brown and T.~C. Koopmans.
\newblock Computational suggestions for maximizing a linear function subject to
  linear inequalities.
\newblock In T.~C. Koopmans, editor, {\em Activity Analysis of Production and
  Allocation}, pages 377--380. John Wiley \& Sons, New York, 1951.

\bibitem{ipm:Burer1}
S.~Burer and R.~D.~C. Monteiro.
\newblock An efficient algorithm for solving the {MAXCUT} {SDP} relaxation.
\newblock {Manuscript}, School of Industrial and Systems Engineering, Georgia
  Institute of Technology, Atlanta, GA~30332--0205, USA, December 1998.

\bibitem{ipm:Burke1}
J.~V. Burke, A.~A. Goldstein, P.~Tseng, and Y.~Ye.
\newblock Translational cuts for convex minimization.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 57--73. World Scientific Publishing Co., London, United
  Kingdom, 1993.

\bibitem{ipm:Burke2}
J.~V. Burke and S.~R. Xu.
\newblock The global linear convergence of a non--interior path--following
  algorithm for linear complementarity problems.
\newblock {Technical Report}, Department of Mathematics, University of
  Washington, Seattle, WA~98195, USA, December 1996.

\bibitem{ipm:Byrd1}
R.~Byrd, J.~C. Gilbert, and J.~Nocedal.
\newblock A trust region method based on interior point technique for nonlinear
  programming.
\newblock {Technical Report} OTC\,96--02, Optimization Technology Center,
  Northwestern University, Evanston, IL~60208--3119, USA, 1996.

\bibitem{ipm:Byrd2}
R.~Byrd, M.~B. Hribar, and J.~Nocedal.
\newblock An interior point algorithm for large scale nonlinear programming.
\newblock {Technical Report} OTC\,97/05, Optimization Technology Center,
  Northwestern University, Evanston, IL~60208--3119, USA, July 1997.

\bibitem{ipm:Byrd3}
R.~Byrd, G.~Liu, and J.~Nocedal.
\newblock On the local behavior of an interior point method for nonlinear
  programming.
\newblock {Technical Report} OTC\,98/02, Optimization Technology Center,
  Northwestern University, Evanston, IL~60208--3119, USA, January 1998.
\newblock To appear in {\em Proceedings of the 1997 Dundee Conference on
  Numerical Analysis}.

\bibitem{ipm:Cao1}
M.~Cao and M.~C. Ferris.
\newblock Interior--point algorithms for monotone affine variational
  inequalities.
\newblock {\em Journal of Optimization Theory and Applications}, 83:269--283,
  1994.

\bibitem{ipm:Carmona1}
R.~A. Carmona and S.~Zhong.
\newblock Interior point methods for sea--bottom image enhancement.
\newblock {\em Proceedings of the Detection and Remediation Technologies for
  Mines and Minelike Targets}, pages 132--137, 1997.

\bibitem{ipm:Carolan1}
W.~Carolan, J.~Hill, J.~Kennington, S.~Niemi, and S.~Wichmann.
\newblock An empirical evaluation of the {KORBX} algorithms for military
  airlift applications.
\newblock {\em Operations Research}, 38:240--248, 1990.

\bibitem{ipm:Caroll1}
C.~W. Caroll.
\newblock The created response surface technique for optimizing nonlinear
  restrained systems.
\newblock {\em Operations Research}, 9(2):169--184, 1961.

\bibitem{ipm:Caron1}
R.~J. Caron and W.~T. Obuchowska.
\newblock Quadratically constrained convex quadratic programmes\,:\,{Faulty}
  feasible regions.
\newblock {Windsor Mathematics StatisticsReport} WMSR 92--05, Department of
  Mathematics, University of Windsor, Windsor, Ontario, Canada~N9B\,3P4, August
  1992.

\bibitem{ipm:Carpenter4}
T.~J. Carpenter.
\newblock {\em Practical interior--point methods for quadratic programming}.
\newblock PhD thesis, School of Engineering and Applied Science, Department of
  Civil Engineering and Operations Research, Princeton University, Princeton,
  NJ~08544, USA, 1992.

\bibitem{ipm:Carpenter1}
T.~J. Carpenter, I.~J. Lustig, J.~M. Mulvey, and D.~F. Shanno.
\newblock A primal--dual interior point method for convex separable nonlinear
  programs.
\newblock {RUTCOR Research Report} RRR~25--90, RUTCOR\,--\,Rutgers Center for
  Operations Research, Hill Center for Mathematical Sciences, New Brunswick,
  NJ~08903, USA, May 1990.
\newblock Technical Report SOR~90--02, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1990.

\bibitem{ipm:Carpenter2}
T.~J. Carpenter, I.~J. Lustig, J.~M. Mulvey, and D.~F. Shanno.
\newblock Higher order predictor--corrector interior point methods with
  application to quadratic objectives.
\newblock {\em SIAM Journal on Optimization}, 3:696--725, 1993.

\bibitem{ipm:Carpenter3}
T.~J. Carpenter, I.~J. Lustig, J.~M. Mulvey, and D.~F. Shanno.
\newblock Separable quadratic programming via primal--dual interior point
  method and its use in a sequential procedure.
\newblock {\em ORSA Journal on Computing}, 5:182--191, 1993.

\bibitem{ipm:Carpenter5}
T.~J. Carpenter and D.~F. Shanno.
\newblock An interior point method for quadratic programs based on conjugate
  projected gradients.
\newblock {\em Computational Optimization and Applications}, 2:5--28, 1993.

\bibitem{ipm:Castillo1}
I.~Castillo and E.~R. Barnes.
\newblock On the convergence of the affine scaling linear programming
  algorithm.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Institute of Technology, Atlanta, GA~30332--0205, USA, April 1995.

\bibitem{ipm:Castro4}
J.~Castro.
\newblock An implementation of a higher--order primal--dual interior point
  algorithm using a predictor--corrector method for linear programming.
\newblock {\em Q{\"u}estii{\'o}}, 22:103--116, 1998.
\newblock (In Spanish, English summary).

\bibitem{ipm:Castro5}
J.~Castro.
\newblock An interior--point algorithm for quadratic programming through
  separable equivalent problems.
\newblock {\em Q{\"u}estii{\'o}}, 22:117--142, 1998.
\newblock (In Spanish, English summary).

\bibitem{ipm:Castro3}
J.~Castro.
\newblock A specialized interior point algorithm for multicommodity flows.
\newblock {Manuscript}, Department of Statistics and Operations Research,
  Universitat Rovira i Virgili, E--43006\,Tarragona, Spain, July 1998.

\bibitem{ipm:Castro1}
J.~Castro and N.~Nabona.
\newblock An implementation of linear and nonlinear multicommodity network
  flows.
\newblock {\em European Journal of Operational Research}, 92:37--53, 1996.

\bibitem{ipm:Castro2}
J.~Castro and N.~Nabona.
\newblock Primal--dual interior point method for multicommodity network flows
  with side constraints and comparison with alternative methods.
\newblock In J.~Dolezal et~al., editor, {\em System Modelling and Optimization
  (Proceedings of the 17th IFIP Conference, Prague, Czech Republic, July
  1995)}, pages 451--458. Chapman \& Hall, London, Great Britain, 1996.

\bibitem{ipm:Cavalier1}
T.~M. Cavalier and T.~C. Schall.
\newblock Implementing a projective algorithm for solving inequality
  constrained linear programs.
\newblock {IMSE Working Paper} 86--128, Department of Industrial and Management
  Systems Engineering, Pennsylvania State University, University Park,
  PA~16802, USA, 1986.

\bibitem{ipm:Cavalier2}
T.~M. Cavalier and T.~C. Schall.
\newblock Implementing an affine scaling algorithm for linear programming.
\newblock {\em Computers and Operations Research}, 14:341--347, 1987.

\bibitem{ipm:Cavalier3}
T.~M. Cavalier and A.~L. Soyster.
\newblock Some computational experience and a modification of the {Karmarkar}
  algorithm.
\newblock {Working Paper} 85--105, Department of Industrial and Management
  Systems Engineering, Pennsylvania State University, University Park,
  PA~16802, USA, 1985.

\bibitem{ipm:Cazzol1}
M.~V. Cazzol, A.~Garzillo, M.~Innorta, N.~Losignore, and P.~Marannino.
\newblock The solution of the voltage/reactive security problems in {VAr}
  planning and in operation scheduling by the dual affine {Karmarkar}
  algorithm.
\newblock {\em Proceedings of the Eleventh Powr Systems Computation Conference
  (Zurich, Switzerland, 1993)}, 1:403--409, 1994.

\bibitem{ipm:Censor3}
Y.~Censor, A.~N. Iusem, and S.~A. Zenios.
\newblock An interior point method with {Bregman} functions for the variational
  inequality problem with paramonotone operators.
\newblock {\em Mathematical Programming}, 81:373--400, 1998.

\bibitem{ipm:Censor1}
Y.~Censor and A.~Lunt.
\newblock Optimization on '$log~x$' entropy over linear inequality constraints.
\newblock {\em SIAM Journal on Control and Optimization}, 25:921--933, 1987.

\bibitem{ipm:Censor2}
Y.~Censor and S.~A. Zenios.
\newblock {\em Parallel Optimization\,: Theory, Algorithms, and Applications}.
\newblock Oxford University Press, New York, NY, USA, 1997.

\bibitem{ipm:Chandru3}
V.~Chandru.
\newblock Notes on {Karmarkar's} new algorithm for linear programming.
\newblock {Unpublished Memorandum}, Department of Industrial Engineering,
  Purdue University, West Lafayette, IN~47907, USA, 1984.

\bibitem{ipm:Chandru1}
V.~Chandru and B.~Kochar.
\newblock A class of algorithms for linear programming.
\newblock {Research Memorandum} 85--14, Department of Industrial Engineering,
  Purdue University, West Lafayette, IN~47907, USA, 1985.
\newblock Revised 1986.

\bibitem{ipm:Chandru2}
V.~Chandru and B.~Kochar.
\newblock Exploiting special structures using a variant of {Karmarkar's}
  algorithm.
\newblock {Research Memorandum} 86--10, Department of Industrial Engineering,
  Purdue University, West Lafayette, IN~47907, USA, 1986.

\bibitem{ipm:Chang1}
S.~Y. Chang and K.~G. Murty.
\newblock The steepest descent gravitational method for linear programming.
\newblock {\em Discrete Applied Mathematics}, 25:211--239, 1989.

\bibitem{ipm:Charnes1}
A.~Charnes, T.~Song, and M.~Wolfe.
\newblock An explicit solution sequence and convergence of {Karmarkar's}
  algorithm.
\newblock {Research Report} CCS~501, Center for Cybernetic Studies, University
  of Texas, Austin, TX~78712--1177, USA, 1984.

\bibitem{ipm:Chen4}
B.~T. Chen.
\newblock {\em A continuation method for monotone variational inequality and
  complementarity problems\,: {With} application to linear and nonlinear
  programming}.
\newblock PhD thesis, Decision Sciences Department, The Wharton School,
  University of Pennsylvania, Philadelphia, PA, USA, 1990.

\bibitem{ipm:Chen3}
B.~T. Chen.
\newblock Finite convergence of nonsmooth equation based methods for affine
  {VIPs}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Management and Systems, Washington State University,
  Pullman, WA~99104, USA, April 1992.

\bibitem{ipm:Chen5}
C.~Chen and O.~L. Mangasarian.
\newblock A class of smoothing functions for nonlinear and mixed
  complementarity problems.
\newblock {\em Computational Optimization and Applications}, 5:97--138, 1996.

\bibitem{ipm:Anstreicher43}
K.~M. Anstreicher~X. Chen, H.~Wolkowicz, and Y.-X. Yuan.
\newblock Strong duality for a trust--region type relaxation of the quadratic
  assignment problem.
\newblock {Research Report} CORR 98--31, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario~N2L\,3G1, Canada,
  1998.

\bibitem{ipm:Chen1}
S.~Chen.
\newblock Computational experience with the {Karmarkar} algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
  CA, USA}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA, April 1986.

\bibitem{ipm:Chen2}
S.~Chen and D.~N. Lee.
\newblock Supercomputers and an efficient implementation of {Karmarkar's}
  algorithm.
\newblock {Talk held at the SIAM National Meeting on Numerical Analysis in
  Denver, CO, USA}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA, 1987.

\bibitem{ipm:Cheng3}
Y.~C. Cheng, D.~J. Houck, E.~Housos, C.~Huang, M.~S. Meketon, L.~Slutsman,
  R.~Vanderbei, and P.~Wang.
\newblock The {AT~\&~T~KORBX Linear Programming System}\,: {S}ystem
  architecture and performance.
\newblock {Talk held at the 13th International Symposium on Mathematical
  Programming in Tokyo, Japan}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733,
  USA, August 1988.

\bibitem{ipm:Cheng4}
Y.~C. Cheng, D.~J. Houck, J.~M. Liu, M.~S. Meketon, L.~Slutsman, R.~J.
  Vanderbei, and P.~Wang.
\newblock The {AT~\&~T~KORBX System}.
\newblock {\em AT~\&~T Technical Journal}, 68:7--19, 1989.

\bibitem{ipm:Cheng2}
Y.~C. Cheng, J.~M. Liu, M.~Meketon, P.~Wang, R.~Vanderbei, and L.~Slutsman.
\newblock Linear programming algorithms implemented on the {AT~\&~T KORBX
  System}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA, October 1988.

\bibitem{ipm:Cheng1}
Y.~C. Cheng and K.~T. Medhi.
\newblock The {AT\,\&\,T KORBX Linear Programming System}\,: {P}reconditioned
  conjugate gradient implementation.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, AT\,\&\,T Bell Laboratories, Holmdel, NJ~07733, USA, October 1989.

\bibitem{ipm:Cheng5}
Z.~Y. Cheng and J.~E. Mitchell.
\newblock An alternative derivation of the projective interior point method for
  linear programming through the least squares approach.
\newblock {\em Optimization}, 31:95--106, 1994.

\bibitem{ipm:Cheng6}
Z.~Y. Cheng and J.~E. Mitchell.
\newblock A primal--dual interior--point method for linear programming based on
  a weighted barrier function.
\newblock {\em Journal of Optimization THeory and Applications}, 87:301--321,
  1995.

\bibitem{ipm:Chifflet1}
M.~J. Chifflet, A.~Lisser, D.~Tachat, and P.~Tolla.
\newblock Computing block--angular {Karmarkar} projections with applications to
  multicommodity flow problems.
\newblock {Talk held at the 12th Triennial Conference on Operations Research in
  Athens, Greece}, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, June 1990.

\bibitem{ipm:Chiment1}
J.~J. Chiment.
\newblock Complexity issues for numerical optimization.
\newblock {\em SIAM News}, 24(3):24--25, May 1991.

\bibitem{ipm:Chin1}
P.~Chin and A.~Vannelli.
\newblock Interior point methods for placement.
\newblock {\em IEEE International Symposium on Circuits and Systems},
  1:1.169--1.172, 1994.

\bibitem{ipm:Chin2}
P.~Chin and A.~Vannelli.
\newblock {PCG} techniques for interior point algorithms.
\newblock {\em Proceedings of the 36th Midwest Symposium on Circuits and
  Systems (Detroit, MI, USA, August 1993)}, 1:200--201, 1994.

\bibitem{ipm:Chiu1}
S.~S. Chiu and Y.~Ye.
\newblock Recovering the shadow price in projection methods for linear
  programming.
\newblock {Technical Report}, Engineering Economic Systems Department, Stanford
  University, Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Chiu2}
S.~S. Chiu and Y.~Ye.
\newblock Simplex method and {Karmarkar's} algorithm\,: {A} unifying structure.
\newblock {Technical Report}, Engineering Economic Systems Department, Stanford
  University, Stanford, CA~94305, USA, 1985/86.

\bibitem{ipm:Choi8}
I.~C. Choi.
\newblock {\em Interior point methods for solving large structured linear
  programs}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Research, Columbia University, New York, NY~10027, USA, 1990.

\bibitem{ipm:Choi6}
I.~C. Choi.
\newblock Partitioning methods in interior point algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Industrial Engineering, The Wichita State University,
  Wichita, KS~67206, USA, April 1992.

\bibitem{ipm:Choi1}
I.~C. Choi and D.~Goldfarb.
\newblock Interior point methods for solving structured linear programs using
  parallel computation.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, October 1989.

\bibitem{ipm:Choi2}
I.~C. Choi and D.~Goldfarb.
\newblock Detecting optimal basic and nonbasic variables prior to optimality in
  interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, May 1990.

\bibitem{ipm:Choi5}
I.~C. Choi and D.~Goldfarb.
\newblock Solving multicommodity network flow problems by an interior point
  method.
\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
  Optimization, Papers from the Workshop held at Cornell University, Ithaca,
  NY, USA, October 1989}, volume~46 of {\em SIAM Proceedings in Applied
  Mathematics}, pages 58--69. Society of Industrial and Applied Mathematics
  (SIAM), Philadelphia, PA, USA, 1990.

\bibitem{ipm:Choi7}
I.~C. Choi and D.~Goldfarb.
\newblock Exploiting special structure in a primal--dual path--following
  algorithm.
\newblock {\em Mathematical Programming}, 58:33--52, 1993.

\bibitem{ipm:Choi9}
I.~C. Choi and D.~Goldfarb.
\newblock On solution--containing ellipsoids in linear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 80:161--173,
  1994.

\bibitem{ipm:Choi3}
I.~C. Choi, C.~L. Monma, and D.~F. Shanno.
\newblock Computational experience with a primal--dual interior point method
  for linear programming.
\newblock {Technical Report}, RUTCOR Center of Operations Research, Rutgers
  University, New Brunswick, NJ~08903, USA, 1989.

\bibitem{ipm:Choi4}
I.~C. Choi, C.~L. Monma, and D.~F. Shanno.
\newblock Further development of a primal--dual interior point method.
\newblock {\em ORSA Journal on Computing}, 2:304--311, 1990.

\bibitem{ipm:Christensen1}
P.~W. Christensen, A.~Larbring, J.~S. Pang, and N.~Stromberg.
\newblock Formulationa nd comparison of algorithm for frictional contact
  problems.
\newblock {\em International Journal for Numerical Methods in Engineering},
  42:145--173, 1998.

\bibitem{ipm:Christiansen1}
E.~Christiansen and K.~O. Kortanek.
\newblock Computing material collapse displacement fields on a {Cray~X--MP/48}
  by the {LP} primal affine scaling algorithm.
\newblock {\em Annals of Operations Research}, 22:355--376, 1990.

\bibitem{ipm:Christiansen2}
E.~Christiansen and K.~O. Kortanek.
\newblock Computation of the collapse state in limit analysis using the {LP}
  primal affine scaling algorithm.
\newblock {\em Journal of Computational and Applied Mathematics}, 34:47--63,
  1991.

\bibitem{ipm:Christoforidis1}
M.~Christoforidis, M.~Aganagic, B.~Awobamise, and S.~Tong.
\newblock Long--term/midterm resource optimization of a hydro--dominant power
  system using interior point method.
\newblock {\em Power Industry Computer Application Conference}, pages 164--,
  1995.

\bibitem{ipm:Christoforidis2}
M.~Christoforidis, M.~Aganagic, B.~Awobamise, S.~Tong, and A.~F. Rahimi.
\newblock Long--term/midterm resource optimization of a hydro--dominant power
  system using interior point method.
\newblock {\em IEEE Transactions on Power Systems}, 11:287--294, 1996.

\bibitem{ipm:Chu1}
S.~C.~K. Chu.
\newblock On the existence of positive non--extreme point solutions of linear
  programming.
\newblock {\em International Journal of Mathematical Education in Science and
  Technology}, 21:99--103, 1990.

\bibitem{ipm:Clark1}
C.~E. Clark and J.~L. Strand.
\newblock Application of the {Karmarkar} algorithm and expert system technology
  to transmission network planning.
\newblock {\em GLOBECOM Tokyo~'87\,: Conference Record of the IEEE/IEICE Global
  Telecommunications Conference in Tokyo}, 2:270, 1987.

\bibitem{ipm:Clausen1}
J.~Clausen and F.~A. {Al--Khayyal}.
\newblock {\em Interior Point Methods}, volume~19 of {\em Mathematical
  Programming Society Committee on Algorithms (COAL) Newsletter}.
\newblock Mathematical Programming Society, Amsterdam, The Netherlands, August
  1991.

\bibitem{ipm:Clements1}
K.~A. Clements, P.~W. Davis, and K.~P. Frey.
\newblock An interior point algorithm for weighted least absolute value power
  system state estimation.
\newblock {\em IEEE Winter Power Meeting (New York 1991)}, pages
  Paper.91--WM225--2 PWRS, 1991.

\bibitem{ipm:Coleman1}
T.~Coleman and Y.~Li.
\newblock Quadratic interior point algorithms for piecewise linear problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, School of Operations Research and Industrial Engineering, Cornell
  University, Ithaca, NY~14853, USA, October 1989.

\bibitem{ipm:Coleman9}
T.~F. Coleman, J.~Czyzyk, C.~Sun, M.~Wagner, and S.~J. Wright.
\newblock {pPCx}\,: {Parallel} software for linear programming.
\newblock {Technical Report} TR\,96--14, Computer Science Department, Cornell
  University, Ithaca, NY~14853, USA, December 1996.
\newblock See also {\it{Proceedings of the Eighth SIAM Conference on Parallel
  Processing for Scientific Computing (Minneapolis, MN, 1997), 8pp.
  (electronic), SIAM, Philadelphia, PA, 1997}}.

\bibitem{ipm:Coleman7}
T.~F. Coleman and L.~A. Hulbert.
\newblock A globally and superlinearly convergent algorithm for convex
  quadratic programs with simple bounds.
\newblock {\em SIAM Journal on Optimization}, 3:298--321, 1993.

\bibitem{ipm:Coleman2}
T.~F. Coleman and Y.~Li.
\newblock {\em Large--Scale Optimization, Papers from the Workshop held at
  Cornell University, Ithaca, NY, USA, October 1989}, volume~46 of {\em SIAM
  Proceedings in Applied Mathematics}.
\newblock Society of Industrial and Applied Mathematics (SIAM), Philadelphia,
  PA, USA, 1990.

\bibitem{ipm:Coleman3}
T.~F. Coleman and Y.~Li.
\newblock A globally and quadratically convergent affine scaling method for
  linear {L$_{\mbox{1}}$} problems.
\newblock {\em Mathematical Programming}, 52:189--222, 1992.

\bibitem{ipm:Coleman4}
T.~F. Coleman and Y.~Li.
\newblock On the convergence of interior--reflective {Newton} methods for
  nonlinear minimization subject to bounds.
\newblock {\em Mathematical Programming}, 67:189--224, 1994.

\bibitem{ipm:Coleman5}
T.~F. Coleman and Y.~Li.
\newblock An interior trust region approach for nonlinear minimization subject
  to bounds.
\newblock {\em SIAM Journal on Optimization}, 6:418--445, 1996.

\bibitem{ipm:Coleman8}
T.~F. Coleman and Y.~Li.
\newblock A reflective {Newton} method for minimizing a quadratic function
  subject to bounds on some of the variables.
\newblock {\em SIAM Journal on Optimization}, 6:1040--1058, 1996.

\bibitem{ipm:Coleman6}
T.~F. Coleman and J.~Liu.
\newblock An interior {Newton} method for quadratic programming.
\newblock {Technical Report} TR\,93--1388, Computer Science Department, Cornell
  University, Ithaca, NY~14853, USA, October 1993.

\bibitem{ipm:Colmenares1}
O.~Colmenares.
\newblock Karmarkar's linear programming algorithm\,: {B}etter or worse than
  the classical method~?
\newblock {Technical Report}, Graduate School of Management, University of
  California at Los Angeles, Los Angeles, CA, USA, January 1985.

\bibitem{ipm:Cominetti1}
R.~Cominetti and J.~{San Martin}.
\newblock Asymptotic analysis of the exponential penalty trajectory in linear
  programming.
\newblock {\em Mathematical Programming}, 67:169--187, 1994.

\bibitem{ipm:Conn4}
A.~R. Conn, N.~I.~M. Gould, and P.~L. Toint.
\newblock A primal--dual algorithm fror minimizing a nonconvex function subject
  to bound and linear equality constraints.
\newblock {Technical Report} RC\,20639, IBM T.\,J.\,Watson Research Center,
  Yorktown Heights, New York, NY, USA, 1996.

\bibitem{ipm:Conn1}
A.~R. Conn, N.~I.~M. Gould, and Ph.~L. Toint.
\newblock A globally convergent {Lagrangian} barrier algorithm for optimization
  with general inequality constraints and simple bounds.
\newblock {Technical Report} 92/07, Department of Mathematics, FUNDP, Namur,
  Belgium, 1992.

\bibitem{ipm:Conn2}
A.~R. Conn, N.~I.~M. Gould, and Ph.~L. Toint.
\newblock A note on using alternative second--order models for the subproblems
  arising in barrier function methods for minimization.
\newblock {\em Numerische Mathematik}, 68:17--33, 1994.

\bibitem{ipm:Conn3}
A.~R. Conn and M.~L. Overton.
\newblock A primal--dual interior--point method for minimizing a sum of
  {Euclidean} distances.
\newblock {Technical Report}, Department of Mathematics, FUNDP, Namur, Belgium,
  1995.
\newblock (In preparation).

\bibitem{ipm:Conway1}
R.~Conway and M.~Magazine.
\newblock A case against software patents.
\newblock {\em OR/MS Today}, 18(1):14--15, February 1991.

\bibitem{ipm:Cook1}
T.~M. Cook and R.~A. Russell.
\newblock {\em Introduction to Management Science}, chapter 4\,: {A}n
  alternative to the simplex method --- {Karmarkar's} algorithm, pages
  137--139.
\newblock Prentice Hall, Englewood Cliffs, NJ~07632, USA, fourth edition, 1989.

\bibitem{ipm:Cottle1}
R.~Cottle, J.-S. Pang, and R.~E. Stone.
\newblock {\em {The Linear Complementarity Problem}}, chapter 5.9\,:
  Interior--point methods, pages 461--475.
\newblock Academic Press, 1992.

\bibitem{ipm:CPLEX1}
{\emph{CPLEX User's Guide}}.
\newblock Manual, CPLEX Optimization, Inc., Incline Village, NV, USA, 1993.

\bibitem{ipm:Cremonese1}
P.~Cremonese.
\newblock Programmazione lineare e algoritmo proiettivo. {Implementazione},
  experienze, relazione col simplesso {(Linear Programming and Projective
  Algorithm. Implementation, experiences, Simplex Relation)}.
\newblock {\em Ricerca Operativa (Italy)}, 18:73--102, 1988.
\newblock (In Italian).

\bibitem{ipm:Crouzeix1}
J.~P. Crouzeix and C.~Roos.
\newblock On the inverse target map of a linear programming problem.
\newblock {Working Paper}, University of Clermont, Clermont, France, 1994.

\bibitem{ipm:Cvetkovic1}
D.~Cvetkovi{\'c}, M.~Cangalovi{\'c}, and V.~V.
  {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Semidefinite relaxations of traveling salesman problem.
\newblock {Technical Report} 902--98, Laboratory for Operations Research,
  Faculty of Organizational Sciences, University of Belgrade, Belgrade,
  Yugoslavia, November 1998.

\bibitem{ipm:Czyzyk2}
J.~Czyzyk, R.~Fourer, and S.~Mehrotra.
\newblock Using massively parallel processors to solve large sparse linear
  programs by an interior--point method.
\newblock {Technical Report}, Department of Industrial Engineering and
  Management Sciences, Northwestern University, Evanston, IL~60208--3119, USA,
  July 1994.
\newblock Revised May 1994.

\bibitem{ipm:Czyzyk1}
J.~Czyzyk, R.~Fourer, and S.~Mehrotra.
\newblock A study of the augmented system and column--splitting approaches for
  solving two--stage stochastic linear programs by interior--point methods.
\newblock {\em ORSA Journal on Computing}, 7:474--490, 1995.

\bibitem{ipm:Czyzyk4}
J.~Czyzyk, S.~Mehrotra, M.~Wagner, and S.~J. Wright.
\newblock {PCx User's Guide (Version 1.1)}.
\newblock {Technical Report} OTC\,96/01, Optimization Technology Center,
  Northwestern University, Evanston, IL~60208--3119, USA, November 1997.
\newblock (Revised version of Czyzyk, Fourer and Wright \cite{ipm:Czyzyk3}).

\bibitem{ipm:Czyzyk3}
J.~Czyzyk, S.~Mehrotra, and S.~J. Wright.
\newblock {PCx} user guide.
\newblock {Technical Report} OTC\,96/01, Optimization Technology Center,
  Northwestern University, Evanston, IL~60208--3119, USA, May 1996.
\newblock For a revised version see Czyzyk et al.\,\cite{ipm:Czyzyk4}.

\bibitem{ipm:Dantzig4}
G.~B. Dantzig.
\newblock Dikin's interior method for {LP}.
\newblock {Manuscript}, Systems Optimization Laboratory, Department of
  Operations Research, Stanford University, Stanford, CA~94305, USA, 1988.

\bibitem{ipm:Dantzig2}
G.~B. Dantzig, D.~Goldfarb, E.~Lawler, C.~Monma, and S.~M. Robinson.
\newblock Report of the {Committee on Algorithms and the Law}.
\newblock {\em Optima (The Mathematical Programming Society Newsletter)},
  33:2--19, June 1991.
\newblock Containing\,: B.~Kahin, The case against {''software patents''},
  Appendix~A, pages 5--13, and The League for Programming Freedom, Against
  software patents, Appendix~B, pages 14--19.

\bibitem{ipm:Dantzig5}
G.~B. Dantzig, D.~Goldfarb, E.~Lawler, C.~Monma, and S.~M. Robinson.
\newblock Report of the {MPS Committee on Algorithms and the Law}.
\newblock {\em SIAM News}, 24(6):3, 18, November 1991.

\bibitem{ipm:Dantzig6}
G.~B. Dantzig and M.~Thapa.
\newblock {\em Linear Programming\,: An Introduction}.
\newblock Springer Verlag, Berlin, Germany, 1997.

\bibitem{ipm:Dantzig1}
G.~B. Dantzig and Y.~Ye.
\newblock A build--up interior method for linear programming\,: {Affine}
  scaling form.
\newblock {Technical Report} SOL~90--4, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, February 1990.

\bibitem{ipm:Dantzig3}
G.~B. Dantzig and Y.~Ye.
\newblock A build--up interior method for linear programming\,: {Affine}
  scaling form.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, July 1991.

\bibitem{ipm:Das1}
I.~Das.
\newblock An interior point algorithm for the general nonlinear programming
  problem with trust region globalization.
\newblock {Technical Report} TR~96--17, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1996.

\bibitem{ipm:David1}
{David~II}-Report.
\newblock Renewing {U.S.} mathematics --- {A} plan for the 1990s,
  {S}ection~24\,: {Interior} point methods for linear programming.
\newblock {\em Notices of the American Mathematical Society}, 37(8):984--1004,
  esp.\ 1001--1002, October 1990.

\bibitem{ipm:Dennis3}
J.~E. Dennis, M.~Heinkenschloss, and L.~N. Vicente.
\newblock Trust--region interior--point algorithms for a class of nonlinear
  programming problems.
\newblock {Technical Report} TR~94--45, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1994.
\newblock Revised May 1995.

\bibitem{ipm:Dennis4}
J.~E. Dennis, M.~Heinkenschloss, and L.~N. Vicente.
\newblock {TRICE}\,--\,{Trust--region} interior--point algorithms for optimal
  control and engineering design problems.
\newblock {Project}, Department of Computational and Applied Mathematics, Rice
  University, Houston, TX~77251, USA, 1997.
\newblock For further informations see {\tt http://www.caam.rice.edu/~trice}.

\bibitem{ipm:Dennis5}
J.~E. Dennis, M.~Heinkenschloss, and L.~N. Vicente.
\newblock Trust--region interior--point {SQP} algorithms for a class of
  nonlinear programming problems.
\newblock {\em SIAM Journal on Control and Optimization}, 36:1750--1794, 1998.

\bibitem{ipm:Dennis1}
J.~E. Dennis, A.~M. Morshedi, and K.~Turner.
\newblock A variable metric variant of the {Karmarkar} algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 39:1--20, 1987.

\bibitem{ipm:Dennis2}
J.~E. Dennis and L.~N. Vicente.
\newblock Trust--region interior--point algorithms for minimization problems
  with simple bounds.
\newblock {\em Applied Mathematics and Parallel Computing}, pages 97--107,
  1996.

\bibitem{ipm:Derigs1}
U.~Derigs.
\newblock {Neuere Ans{\"a}tze in der Linearen Optimierung---Motivation,
  Konzepte und Verfahren~(Recent results in linear programming---motivation,
  concepts and methods)}.
\newblock In L.~Streitfeldt, H.~Hauptmann, A.~W. Marusev, D.~Ohse, and U.~Pape,
  editors, {\em Operations Research Proceedings 1985}, pages 47--58, Springer
  Verlag, Berlin, Germany, 1986.
\newblock (In German).

\bibitem{ipm:Diao1}
Z.~Y. Diao.
\newblock Karmarkar's algorithm and its modification.
\newblock {\em Chinese Journal on Operations Research}, 7(1):73--75, 1988.

\bibitem{ipm:Diao2}
Z.~Y. Diao.
\newblock A remark on {Karmarkar's} algorithm.
\newblock {\em Chinese Journal on Operations Research}, 7(2):61--62, 1988.

\bibitem{ipm:Diao3}
Z.~Y. Diao.
\newblock Interior point algorithms and dynamic systems.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Shandong University, People's Republic of China, May 1992.

\bibitem{ipm:Didderich1}
G.~T. Didderich.
\newblock Some remarks on {Karmarkar's} potential function.
\newblock {\em Aequationes Mathematicae}, 36:57--75, 1988.

\bibitem{ipm:Dikin1}
I.~I. Dikin.
\newblock Iterative solution of problems of linear and quadratic programming.
\newblock {\em Doklady Akademii Nauk SSSR}, 174:747--748, 1967.
\newblock Translated in\,: {\em Soviet Mathematics Doklady 8:674--675, 1967}.

\bibitem{ipm:Dikin2}
I.~I. Dikin.
\newblock On the convergence of an iterative process.
\newblock {\em Upravlyaemye Sistemi}, 12:54--60, 1974.
\newblock (In Russian).

\bibitem{ipm:Dikin3}
I.~I. Dikin.
\newblock Letter to the editor.
\newblock {\em Mathematical Programming}, 41:393--394, 1988.

\bibitem{ipm:Dikin5}
I.~I. Dikin.
\newblock The convergence of dual variables.
\newblock {Technical Report}, Siberian Energy Institute, Irkutsk, Russia,
  December 1991.

\bibitem{ipm:Dikin6}
I.~I. Dikin.
\newblock Determination of the interior point of one system of linear
  inequalities.
\newblock {\em Kibernetika Sistemnyi Analiz}, 1:76--74, 188, 1992.
\newblock (In Russian). Translated in Cybernetic and Systems Analysis.

\bibitem{ipm:Dikin8}
I.~I. Dikin.
\newblock The method of interior points in linear programming.
\newblock In V.~P. Bulatov, editor, {\em {Optimizatsiya\,: Modeli, Metody,
  Resheniya}}, pages 54--69. Nauka, Novosibirsk, USSR, 1992.
\newblock (In Russian).

\bibitem{ipm:Dikin7}
I.~I. Dikin and C.~Roos.
\newblock Convergence of the dual variables for the primal affine scaling
  method with unit steps in the homogeneous case.
\newblock {\em Journal of Optimization Theory and Applications}, 95:305--321,
  1997.

\bibitem{ipm:Dikin4}
I.~I. Dikin and V.~I. Zorkaltsev.
\newblock {\em Iterative Solutions of Mathematical Programming Problems --
  Interior Point Methods}.
\newblock Nauka Publishers, Novosibirsk, USSR, 1980.
\newblock (In Russian).

\bibitem{ipm:Ding4}
J.~Ding.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {Technical Report}, Department of Mathematics, Michigan State
  University, East Lansing, MI~48824, USA, 1988.

\bibitem{ipm:Ding3}
J.~Ding.
\newblock An interior point algorithm for linear complementarity problems.
\newblock {Technical Report}, University of Southern Mississippi, USA, 1992.
\newblock To appear in {\em Linear Algebra and Its Applications}.

\bibitem{ipm:Ding5}
J.~Ding.
\newblock A scaled gradient projection algorithm for linear complementarity
  problems.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 58--67. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Ding1}
J.~Ding and T.~Y. Li.
\newblock An algorithm based on weighted logarithmic barrier functions for
  linear complementarity problems.
\newblock {\em Arabian Journal for Science and Engineering}, 15(4):769--685,
  1990.

\bibitem{ipm:Ding2}
J.~Ding and T.~Y. Li.
\newblock A polynomial--time predictor--corrector algorithm for a class of
  linear complementarity problems.
\newblock {\em SIAM Journal on Computing}, 1(1):83--92, 1991.

\bibitem{ipm:Dinn1}
J.~Dinn.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {Technical Report}, Department of Mathematics, Michigan State
  University, East Lansing, MI~48824, USA, 1988.
\newblock Incorrect author name, see Ding \cite{ipm:Ding4}.

\bibitem{ipm:Dinn2}
N.~F. Dinn, N.~K. Karmarkar, and L.~P. Sinha.
\newblock Karmarkar algorithm enables interactive planning of networks.
\newblock {\em Record AT~\&~T~Bell Laboratories}, 64(2):11--13, 1986.

\bibitem{ipm:Dodani1}
M.~H. Dodani and A.~J.~G. Babu.
\newblock Karmarkar's projective method for linear programming\,: {A}
  computational survey.
\newblock {\em Computers and Industrial Engineering}, 13:285--289, 1987.

\bibitem{ipm:Dodani2}
M.~H. Dodani and A.~J.~G. Babu.
\newblock Karmarkar's projective method for linear programming\,: {A}
  computational appraisal.
\newblock {\em Computers and Industrial Engineering}, 16:198--206, 1989.

\bibitem{ipm:Dodani3}
M.~H. Dodani and A.~J.~G. Babu.
\newblock Karmarkar's projective method for linear programming\,: {A}
  computational survey.
\newblock {\em International Journal of Mathematical Education in Science and
  Technology}, 21:191--212, 1990.

\bibitem{ipm:Dolecki1}
S.~Dolecki.
\newblock {\em Optimization\,: Proceedings of the 5th French--German Conference
  in Castel--Novel, Varetz, France, October 1988}, volume 1405 of {\em Lecture
  Notes in Mathematics}.
\newblock Springer Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Doljansky1}
M.~Doljansky and M.~Teboulle.
\newblock An interior proximal algorithm and the exponetial multiplier method
  for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 9:1--13, 1999.

\bibitem{ipm:Domich1}
P.~D. Domich, P.~T. Boggs, J.~R. Donaldson, and C.~Witzgall.
\newblock Optimal 3--dimensional methods for linear programming.
\newblock {Technical Report} NISTIR~89--4225, United States Department of
  Commerce, National Institute of Standards and Technology, Gaithersburg,
  MD~20899, USA, December 1989.

\bibitem{ipm:Domich3}
P.~D. Domich, P.~T. Boggs, J.~R. Donaldson, and C.~Witzgall.
\newblock Third order correction methods to the method of centers for linear
  programming problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, United States Department of Commerce, National Institute of Standards
  and Technology, Applied and Computational Mathematics Division, Boulder,
  CO~80303, USA, May 1990.

\bibitem{ipm:Domich4}
P.~D. Domich, P.~T. Boggs, J.~R. Donaldson, and C.~Witzgall.
\newblock An interior point approach for linear and quadratic programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, United States Department of Commerce, National Institute of Standards
  and Technology, Applied and Computational Mathematics Division, Boulder,
  CO~80303, USA, November 1991.

\bibitem{ipm:Domich2}
P.~D. Domich, P.~T. Boggs, J.~E. Rogers, and C.~Witzgall.
\newblock Optimizing over 3--d subspaces in an interior point method.
\newblock {\em Linear Algebra and Its Applications}, 152:315--342, 1991.

\bibitem{ipm:Doup1}
T.~Doup, R.~Bisseling, and L.~Loyens.
\newblock A parallel interior point algorithm for linear programming on a
  network of 400 transputers.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom}, Shell
  Research Center (KSLA), Amsterdam, The Netherlands, January 1991.
\newblock See also Bisseling, Doup and Loyens\,\cite{ipm:Bisseling1}.

\bibitem{ipm:Dowling1}
M.~L. Dowling.
\newblock Comparing the affine and projective vector fields associated with
  linear programming.
\newblock {Technical Report}, Department of Management, University of Georgia,
  Athens, GA~30602, USA, 1989.
\newblock Submitted to {\em Mathematical Programming}.

\bibitem{ipm:Dowling3}
M.~L. Dowling.
\newblock An affine scaling method for nonlinear programming.
\newblock {Habilitationthesis}, Institut f{\"u}r Angewandte Mathematik,
  Abteilung f{\"u}r Mathematische Optimierung, Technische Universit{\"a}t
  Braunschweig, P{\"o}ckelstr. 14, D--38106 Braunschweig, Germany, 1994.

\bibitem{ipm:Dowling2}
M.~L. Dowling.
\newblock An affine scaling algorithm for linear programming problems with
  inequality constraints.
\newblock {\em Mathematical Models of Operations Research}, 43:301--318, 1996.

\bibitem{ipm:Du1}
D.~Z. Du, F.~Wu, and X.~S. Zhang.
\newblock Why is the objective function nonlinearized in the interior point
  methods for nonlinear programming?
\newblock {\em Mathematics in Practice and Theory}, 2:63--68, 1990.
\newblock (In Chinese).

\bibitem{ipm:Duff1}
I.~S. Duff.
\newblock The solution of large--scale least--squares problems on
  supercomputers.
\newblock {\em Annals of Operations Research}, 22:241--252, 1990.

\bibitem{ipm:Zhang24}
D.Zhang and Y.~Zhang.
\newblock On constructing interior--point path--following methods for certain
  semimonotone complemntarity problems.
\newblock {Technical Report} TR~97--19, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1997.

\bibitem{ipm:Eckstein1}
J.~Eckstein, R.-J. Qi, V.~I. Ragulin, and S.~A. Zenios.
\newblock Data--parallel implementations of dense linear programming
  algorithms.
\newblock {Technical Report} TMC--230, Thinking Machines Corporation,
  Cambridge, MA~02142, USA, May 1992.
\newblock Also available as Decision Sciences Department Report~92--05--06, The
  Wharton School, University of Pennsylvania, Philadelphia, PA~19101, USA.

\bibitem{ipm:Economist1}
Not so simplex.
\newblock {\em The Economist}, December 1, 1984.

\bibitem{ipm:Edirisinghe1}
C.~Edirisinghe and W.~Ziemba.
\newblock A boundary point algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Commerce and Business Administration, University of
  British Columbia, Vancouver, BC~V6T~1Y8, Canada, November 1991.

\bibitem{ipm:Edwards1}
J.~J. Edwards and J.~A. Tomlin.
\newblock Towards a highly parallel mathematical programming system.
\newblock {Talk held at the 14th International Mathematical Programming
  Symposium in Amsterdam, The Netherlands}, IBM Almaden Research Center, San
  Jose, CA~95120, USA, August 1991.
\newblock {Technical Report in preparation}.

\bibitem{ipm:ElBakry4}
A.~S. {El--Bakry}.
\newblock {\em On the role of indicators in identifying zero variables in
  linear programming}.
\newblock PhD thesis, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, 1991.

\bibitem{ipm:ElBakry8}
A.~S. {El--Bakry}.
\newblock Convergence rate of primal--dual reciprocal barrier {Newton}
  interior--point methods.
\newblock {\em Optimization Methods and Software}, 9:37--44, 1998.

\bibitem{ipm:ElBakry6}
A.~S. {El--Bakry}, R.~A. Tapia, T.~Tsuchiya, and Y.~Zhang.
\newblock On the formulation and theory of the {Newton} interior--point method
  for nonlinear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 89:507--541,
  1996.

\bibitem{ipm:ElBakry2}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock Numerical comparisons of local convergence strategies for
  interior--point methods in linear programming.
\newblock {Technical Report} TR~91--18, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:ElBakry3}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock On obtaining highly accurate or basic solutions using interior--point
  methods in linear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Mathematical Sciences, Rice University, Houston,
  TX~77251, USA, May 1992.

\bibitem{ipm:ElBakry7}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock Logarithmic indicators and the identification of subgroups of
  variables in interior--point methods.
\newblock {Technical Report} TR~93--35, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, September 1993.

\bibitem{ipm:ElBakry1}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock A study of indicators for identifying zero variables in
  interior--point methods.
\newblock {\em SIAM Review}, 36:45--72, 1994.

\bibitem{ipm:ElBakry5}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock On the convergence rate of {Newton} interior--point methods in the
  absence of strict complementarity.
\newblock {\em Computational Optimization and Applications}, 6:157--167, 1996.

\bibitem{ipm:Emmett1}
A.~Emmett.
\newblock Karmarkar's algorithm\,: {A} threat to simplex~?
\newblock {\em IEEE Spectrum}, 22(12):54--55, December 1985.

\bibitem{ipm:Encheva1}
T.~J. Encheva.
\newblock Computational comparisons for the method of centers of gravity of
  vertices.
\newblock {\em Serdica (Bulgaricae Mathematicae Publicationes)},
  16(3):188--193, 1990.

\bibitem{ipm:Epelman1}
M.~Epelman and R.~M. Freund.
\newblock Condition number complexity of an elementary algorithm for resolving
  a conic linear system.
\newblock {Technical Report}, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, February 1997.

\bibitem{ipm:Epelman2}
M.~Epelman and R.~M. Freund.
\newblock Condition number complexity of an elementary algorithm for computing
  a reliable solution of a conic linear system.
\newblock {Technical Report}, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, December 1998.

\bibitem{ipm:Eriksson1}
J.~R. Eriksson.
\newblock Algorithms for entropy and mathematical programming.
\newblock {Link{\"o}ping Studies in Science and Technology Dissertations}~63,
  Department of Mathematics, Link{\"o}ping University, S--58183~Link{\"o}ping,
  Sweden, 1981.

\bibitem{ipm:Eriksson2}
J.~R. Eriksson.
\newblock An iterative primal--dual algorithm for linear programming.
\newblock {Technical Report} LiTH--MAT--R--1985--10, Department of Mathematics,
  Link{\"o}ping University, S--58183~Link{\"o}ping, Sweden, 1985.

\bibitem{ipm:Eriksson3}
J.~R. Eriksson.
\newblock Using the entropy function to get an interior point method for linear
  programming.
\newblock {Technical Report} LiTH--MAT--R--1990--02, Department of Mathematics,
  Link{\"o}ping University, S--58183~Link{\"o}ping, Sweden, 1990.

\bibitem{ipm:Evtushenko3}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock {Barrier--Newton} methods in linear programming.
\newblock In J.~Henry and J.~P. Yvon, editors, {\em System Modelling and
  Optimization (Proceedings of the 16th IFIP--TC7 Conference, Compiegne,
  France, July 1993)}, volume 197 of {\em Lecture Notes in Control and
  Information Sciences}, pages 215--224. Springer Verlag, Berlin, Germany,
  1994.

\bibitem{ipm:Evtushenko4}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Stable barrier--projection and barrier--{Newton} methods for linear
  and nonlinear programming.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
  Optimization\,: The State--of--the--Art (Il Ciocco, Barga, Italy, September
  1993)}, volume 434 of {\em NATO Adavanced Science Institute Series C\,:
  Mathematical and Physical Sciences}, pages 255--285. Kluwer Academic
  Publishers, Dordrecht, The Netherlands, 1994.
\newblock See also Evtushenko and Zhadan
  \cite{ipm:Evtushenko1,ipm:Evtushenko2}.

\bibitem{ipm:Evtushenko1}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Stable barrier--projection and barrier--{Newton} methods in linear
  programming.
\newblock {\em Computational Optimization and Applications}, 3:289--303, 1994.
\newblock See also Evtushenko and Zhadan \cite{ipm:Evtushenko4}.

\bibitem{ipm:Evtushenko2}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Stable barrier--projection and barrier--{Newton} methods in nonlinear
  programming.
\newblock {\em Optimization Methods and Software}, 3:237--256, 1994.
\newblock See also Evtushenko and Zhadan \cite{ipm:Evtushenko4}.

\bibitem{ipm:Evtushenko5}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Dual barrier--projection methods in linear programming.
\newblock In R.~P. Agarwal, editor, {\em Recent Trends in Optimization Theory
  and Applications}, volume~5 of {\em World Science Series in Applied
  Analysis}, pages 51--66. World Science Publishing, River Edge, NJ, USA, 1995.

\bibitem{ipm:Evtushenko7}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Dual barrier--projection and {barrier--Newton} methods for linear
  programming problems.
\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
  (Moscow)}, 36(7):30--45, 1996.
\newblock (In Russian).

\bibitem{ipm:Evtushenko8}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock On some papers on interior point methods.
\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
  (Moscow)}, 36(12):161--162, 1996.
\newblock (In Russian).

\bibitem{ipm:Evtushenko6}
Yu.~G. Evtushenko, V.~G. Zhadan, and A.~P. Cherenkov.
\newblock Application of {Newton's} method to the solution of linear
  programming problems.
\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
  (Moscow)}, 35:850--866, 1995.
\newblock Translated in\,: {\em USSR Computational Mathematics and Mathematical
  Physics}, 35:673--686, 1995.

\bibitem{ipm:Ezzine1}
J.~Ezzine and M.~Ben-Daya.
\newblock Singular pertubed nonlinear {ODE}s and interior point optimization
  algorithms.
\newblock {\em Proceedings of the 1995 American Control Conference (Seattle,
  WA, USA, June 1995)}, 3:1816--1820, 1995.

\bibitem{ipm:Fan2}
M.~K.~H. Fan.
\newblock A second--order interior point method for solving linear matrix
  inequality problems.
\newblock {\em SIAM Journal on Control and Optimization}, 19\,?
\newblock (To appear).

\bibitem{ipm:Fan1}
M.~K.~H. Fan and B.~Nekooie.
\newblock A second--order interior point method for solving linear matrix
  inequality problems.
\newblock {\em Proceedings of the 1994 American Control Conference (Baltimore,
  MD, USA, June/July 1994)}, 1:831--835, 1994.
\newblock A different title found\,: {\em An algorithm on minimizing
  generalized eigenvalues with linear matrix inequality constraints}.

\bibitem{ipm:Fang10}
S.-C. Fang.
\newblock Dynamic facility network planning -- {A} solution architecture with
  block {Cholesky} factorization.
\newblock {Technical Memorandum} 54112--860305--01~TM, AT~\&~T Bell
  Laboratories, Holmdel, NJ~07733, USA, March 1986.

\bibitem{ipm:Fang9}
S.-C. Fang.
\newblock Dynamic facility network planning -- {An LP} loader.
\newblock {Technical Memorandum} 54112--860610--01~TM, AT~\&~T Bell
  Laboratories, Holmdel, NJ~07733, USA, June 1986.

\bibitem{ipm:Fang3}
S.-C. Fang.
\newblock A new unconstrained convex programming approach to linear
  programming.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 36(2):149--161, 1992.

\bibitem{ipm:Fang4}
S.-C. Fang and S.~Puthenpura.
\newblock {\em Linear Optimization and Extensions}.
\newblock Prentice Hall, Englewood Cliffs, NJ~07632, USA, 1993.

\bibitem{ipm:Fang2}
S.-C. Fang, S.~C. Puthenpura, R.~Saigal, and P.~Sinha.
\newblock Stochastic linear programming via affine scaling and {Kalman}.
\newblock {Technical Memorandum} 51173--900808--01~TM, AT~\&~T Bell
  Laboratories, Holmdel, NJ~07733, USA, 1989.

\bibitem{ipm:Fang12}
S.-C. Fang and L.~A. Slutsman.
\newblock Dynamic facility network planning -- {Modeling}.
\newblock {Technical Memorandum} 54112--850915--01~TM, AT~\&~T Bell
  Laboratories, Holmdel, NJ~07733, USA, September 1985.

\bibitem{ipm:Fang11}
S.-C. Fang and L.~A. Slutsman.
\newblock Dynamic facility network planning -- {Design} architecture.
\newblock {Technical Memorandum} 54112--860226--01~TM, AT~\&~T Bell
  Laboratories, Holmdel, NJ~07733, USA, February 1986.

\bibitem{ipm:Fang13}
S.-C. Fang and H.~S.~J. Tsao.
\newblock On the entropic perturbation and exponential penalty methods for
  linear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 89:461--466,
  1996.

\bibitem{ipm:Fang5}
S.-C. Fang and J.~H.~S. Tsao.
\newblock Linear programming with an entropic perturbation.
\newblock {OR Research Report} 259, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, October 1991.
\newblock To appear in {\em Zeitscrift f{\"u}r Operations Research -- Methods
  and Model of Operations Research 1993}.

\bibitem{ipm:Fang6}
S.-C. Fang and J.~H.~S. Tsao.
\newblock An unconstrained convex programming approach to solving convex
  quadratic programming problems.
\newblock {OR Research Report} 263, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, April 1992.
\newblock To appear in {\em Optimization, 1992}.

\bibitem{ipm:Fang8}
S.-C. Fang and S.-Y. Wu.
\newblock Entropic path--following for linear semi--infinite programming.
\newblock {OR Research Report} 266, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, December 1992.

\bibitem{ipm:Fang7}
S.-C. Fang and S.-Y. Wu.
\newblock An inexact approach to solving linear semi--infinite programming
  problems.
\newblock {OR Research Report} 265, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, November 1992.

\bibitem{ipm:Fang1}
W.~Fang and W.~Shi-Quan.
\newblock New algorithms for linear programming.
\newblock {Technical Report}, Institute of Applied Mathematics, Academia
  Sinica, Beijing, People Republic of China, 19..(?).

\bibitem{ipm:Farrell1}
J.~J. Farrell.
\newblock Recent advances in linear programming applied to global defense.
\newblock {\em Proceedings of the 27th IEEE Conference on Decision and Control,
  Austin, TX, USA}, pages 242--243, December 1988.

\bibitem{ipm:Fask1}
A.~Fask and W.~F. Walker.
\newblock A polynomial--time algorithm for solving transportation problems
  where the sources are bounded.
\newblock {Talk held at ORSA/TIMS Joint National Meeting in New Orleans, USA},
  Farleigh Dickinson University, Madison, NJ~07940, USA, May 1987.

\bibitem{ipm:Faybusovich9}
F.~Faybusovich.
\newblock On the phase portrait of the {Karmarkar's} flow.
\newblock In K.~L. Bowers, editor, {\em Computation and Control\,III
  (Proceedings of the Third Bozeman Conference, Bozeman, MT, USA, August 1992},
  volume~15 of {\em Progress in Systems and Control Theory}, pages 203--210.
  Birkh{\"a}user Verlag, Basel, Switzerland, 1993.

\bibitem{ipm:Faybusovich1}
L.~E. Faybusovich.
\newblock Interior--point methods and entropy.
\newblock {\em Proceedings of the 30th IEEE Conference on Decision and Control
  (Brighton, United Kingdom, December 1991)}, 3:2094--2095, 1991.

\bibitem{ipm:Faybusovich2}
L.~E. Faybusovich.
\newblock Dikin's algorithm for matrix linear programming problems.
\newblock In J.~Henry and J.~P. Yvon, editors, {\em System Modelling and
  Optimization (Proceedings of the 16th IFIP--TC7 Conference, Compiegne,
  France, July 1993)}, volume 197 of {\em Lecture Notes in Control and
  Information Sciences}, pages 237--247. Springer Verlag, Berlin, Germany,
  1994.

\bibitem{ipm:Faybusovich6}
L.~E. Faybusovich.
\newblock The {Gibbs} variational principle, gradient floes and interior--point
  methods.
\newblock In A.~Bloch, editor, {\em Hamiltonian and Gradient Flows, Algorithms
  and Control}, volume~3 of {\em Fields Institute Communications Series}, pages
  99--111. American Mathematical Society, Providence, Rhode Island, USA, 1994.

\bibitem{ipm:Faybusovich3}
L.~E. Faybusovich.
\newblock A {Hamiltonian} structure for generalized affine--scaling vector
  fields.
\newblock {\em Journal on Nonlinear Sciences}, 5:11--28, 1995.

\bibitem{ipm:Faybusovich7}
L.~E. Faybusovich.
\newblock Jordan algebras, symmetric cones and interior--point methods.
\newblock {Research Report}, Department of Mathematics, University of Notre
  Dame, Notre Dame, IN~46556, USA, November 1995.

\bibitem{ipm:Faybusovich5}
L.~E. Faybusovich.
\newblock On a matrix generalization of affine--scaling vector fields.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 16:886--897,
  1995.

\bibitem{ipm:Faybusovich11}
L.~E. Faybusovich.
\newblock Linear systems in jordan algebras and primal--dual interior--point
  algorithms.
\newblock {Research Report}, Department of Mathematics, University of Notre
  Dame, Notre Dame, IN~46556, USA, August 1996.

\bibitem{ipm:Faybusovich8}
L.~E. Faybusovich.
\newblock Semidefinite programming\,: {A} path--following algorithm for a
  linear--quadratic functional.
\newblock {\em SIAM Journal on Optimization}, 6:1007--1024, 1996.

\bibitem{ipm:Faybusovich13}
L.~E. Faybusovich.
\newblock {Euclidean Jordan} algebras and interior--point methods.
\newblock {Research Report}, Department of Mathematics, University of Notre
  Dame, Notre Dame, IN~46556, USA, June 1997.

\bibitem{ipm:Faybusovich14}
L.~E. Faybusovich.
\newblock Euclidean jordan algebras and generalized affine--scaling vector
  fields.
\newblock {Research Report}, Department of Mathematics, University of Notre
  Dame, Notre Dame, IN~46556, USA, January 1998.

\bibitem{ipm:Faybusovich12}
L.~E. Faybusovich.
\newblock Infinite--dimensional semidefinite programming\,: {Regularized}
  determinants and self--concordant barriers.
\newblock In P.~M. Pardalos and M.~Wolkowicz, editors, {\em Topics in
  Semidefinite and Interior--Point Methods}, volume~18 of {\em Fields Institute
  Communications Series}, pages 39--49. American Mathematical Society (AMS),
  Providence, RI, USA, 1998.

\bibitem{ipm:Faybusovich15}
L.~E. Faybusovich.
\newblock A {Jordan}--algebraic approach to potential--reduction algorithms.
\newblock {Research Report}, Department of Mathematics, University of Notre
  Dame, Notre Dame, IN~46556, USA, April 1998.

\bibitem{ipm:Faybusovich4}
L.~E. Faybusovich and J.~B. Moore.
\newblock Infinite--dimensional quadratic optimization\,: {Interior}--point
  methods and control applications.
\newblock {\em Applied Mathematics and Optimization}, 36:43--66, 1997.

\bibitem{ipm:Faybusovich10}
L.~E. Faybusovich and J.~B. Moore.
\newblock Long step path--following algorithm for the convex quadratic
  programming in a {Hilbert} space.
\newblock {\em Journal of Optimization Theory and Applications}, 95:615--636,
  1997.
\newblock Also published in\,: {\em Proceedings of the 34th IEEE Conference on
  Decision and Control, Part 2/4 (1995), pp.\,1109--1114}.

\bibitem{ipm:Feijoo2}
B.~Feijoo, A.~Sanchez, and C.~C. Gonzaga.
\newblock Interior post--optimality techniques for linear programming\,:
  {Method} of centers.
\newblock {Working Paper}, Departamento de Matematicas Puras y Aplicadas,
  Universidad Simon Bolivar, Apartado Postal~89000, Caracas~1080~A, Venezuela,
  1994.

\bibitem{ipm:Feijoo1}
B.~Feijoo, A.~Sanchez, and C.~C. Gonzaga.
\newblock Maintaining closeness to the analytic center of a polytope by
  perturbing added hyperplanes.
\newblock {\em Applied Mathematics and Optimization}, 35:139--144, 1997.

\bibitem{ipm:Feng1}
G.~Feng and B.~Yu.
\newblock Combined homotopy interior point method for nonlinear programming
  problems.
\newblock In T.~Ushijima, editor, {\em Advances in Numerical Mathematics
  (Proceedings of the Second Japan--China Seminar on Numerical Mathematics,
  August 1994, Tokyo, Japan)}, volume~14 of {\em Lecture Notes in Numerical and
  Applied Analysis}, pages 9--16. 1995.

\bibitem{ipm:Fernandes1}
L.~Fernandes, J.~J. J{\'u}dice, and J.~Patricio.
\newblock An investigation of interior--point and block pivoting algorithms for
  large--scale symmetric monotone linear complementarity problems.
\newblock {\em Computational Optimization and Applications}, 5:49--77, 1996.

\bibitem{ipm:Ferris1}
M.~C. Ferris and A.~B. Philpott.
\newblock On the performance of {Karmarkar's} algorithm.
\newblock {\em Journal of the Operational Research Society}, 39:257--270, 1988.

\bibitem{ipm:Ferris2}
M.~C. Ferris and A.~B. Philpott.
\newblock An interior point algorithm for semi--infinite linear programming.
\newblock {\em Mathematical Programming}, 43:257--276, 1989.

\bibitem{ipm:Ferris3}
M.~C. Ferris and A.~B. Philpott.
\newblock On affine scaling and semi--infinite programming.
\newblock {\em Mathematical Programming}, 52:361--364, 1992.

\bibitem{ipm:Fiacco1}
A.~V. Fiacco.
\newblock Barrier methods in nonlinear programming.
\newblock In A.~Holzman, editor, {\em Operations Research Support Methodology},
  volume~2 of {\em Industrial Engineering Series}, pages 377--440. Marcel
  Dekker, New York, 1979.

\bibitem{ipm:Fiacco2}
A.~V. Fiacco.
\newblock Perturbed variations of penalty function methods --- example\,:
  {Projective SUMT}.
\newblock {\em Annals of Operations Research}, 27:371--380, 1990.

\bibitem{ipm:Fiacco5}
A.~V. Fiacco.
\newblock Objective function and logarithmic barrier function properties in
  convex programmong\,: {Level} sets, solution attainment and strict convexity.
\newblock {\em Optimization}, 34:213--222, 1995.

\bibitem{ipm:Fiacco4}
A.~V. Fiacco and J.~Lin.
\newblock Extension of algorithmic sensitivity calculations in nonlinear
  programming using barrier and penalty functions.
\newblock {Technical Report}, School of Engineering and Applied Science,
  Department of Operations Research, The George Washington University,
  Washington, D.C.~20052, USA, 1994.
\newblock To appear in {\em Optimization}.

\bibitem{ipm:Fiacco3}
A.~V. Fiacco and G.~P. McCormick.
\newblock {\em Nonlinear Programming\,: Sequential Unconstrained Minimization
  Techniques}.
\newblock John Wiley \& Sons, New York, 1968.
\newblock Reprint\,: Volume 4 of {\em SIAM Classics in Applied Mathematics},
  SIAM Publications, Philadelphia, PA~19104--2688, USA, 1990.

\bibitem{ipm:Fischer1}
A.~Fischer.
\newblock On the local superlinear convergence of {Newton}--type method for
  {LCP} under weak conditions.
\newblock {\em Optimization Methods and Software}, 6:83--107, 1995.

\bibitem{ipm:Facchinei1}
F.~Facchineiand~A. Fischer and C.~Kanzow.
\newblock On the identification of zero variables in an interior--point
  framework.
\newblock {Mathematical Programming Technical Report}, Department of Computer
  Sciences, University of Wisconsin, Madison, WI~53706, USA, May 1998.

\bibitem{ipm:Fletcher2}
R.~Fletcher.
\newblock {\em Practical Methods of Optimization}, chapter 8.7\,: {Polynomial}
  time algorithms, pages 183--188.
\newblock John Wiley\,\&\,Sons, New York, second edition, 1987.

\bibitem{ipm:Fletcher1}
R.~Fletcher.
\newblock Recent developments in linear and quadratic programming.
\newblock In A.~Iserles and M.~J.~D. Powell, editors, {\em The
  State--of--the--Art in Numerical Analysis}, pages 213--243, esp.\,219--224.
  Oxford University Press, Oxford, 1987.

\bibitem{ipm:Fliege1}
J.~Fliege and S.~Nickel.
\newblock An interior point method for multifacility location problems with
  forbidden regions.
\newblock {Ergebnisberichte Angewandte Mathematik} 142, Institut f{\"u}r
  Mathematik, Universit{\"a}t Dortmund, Vogelpothsweg~64, Dortmund, Germany,
  1997.

\bibitem{ipm:Forrest1}
J.~J.~H. Forrest and J.~A. Tomlin.
\newblock Vector processing in simplex and interior methods for linear
  programming.
\newblock {\em Annals of Operations Research}, 22:71--100, 1990.

\bibitem{ipm:Forrest2}
J.~J.~H. Forrest and J.~A. Tomlin.
\newblock Implementing interior point linear programming methods in the
  {Optimization Subroutine Library (OSL)}.
\newblock {\em IBM Systems Journal}, 31(1):26--38, 1992.

\bibitem{ipm:Forsgren2}
A.~L. Forsgren.
\newblock On linear least--squares problems with diagonally dominant weight
  matrices.
\newblock {Technical Report} {TRITA--MAT--1995--OS2}, Optimization and Systems
  Theory, Department of Mathematics, Royal Institute of Technology, S--10044
  Stockholm, Sweden, 1995.

\bibitem{ipm:Forsgren5}
A.~L. Forsgren.
\newblock Optimality conditions for nonconvex semidefinite programming.
\newblock {Technical Report} {TRITA--MAT--1998--OS6}, Optimization and Systems
  Theory, Department of Mathematics, Royal Institute of Technology, S--10044
  Stockholm, Sweden, May 1998.

\bibitem{ipm:Forsgren4}
A.~L. Forsgren and P.~E. Gill.
\newblock Primal-dual interior methods for nonconvex nonlinear programming.
\newblock {\em SIAM Journal on Optimization}, 8:1132--1152, 1998.

\bibitem{ipm:Forsgren3}
A.~L. Forsgren, P.~E. Gill, and J.~R. Shinnerl.
\newblock Stability of symmetric ill--conditioned systems arising in interior
  methods for constrained optimization.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 17:187--211,
  1996.

\bibitem{ipm:Forsgren1}
A.~L. Forsgren and W.~Murray.
\newblock Newton methods for large--scale linear equality--constrained
  minimization.
\newblock {Technical Report} SOL~90--6, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, 1990.

\bibitem{ipm:Fourer1}
R.~Fourer and S.~Mehrotra.
\newblock Performance of an augmented system approach for solving
  least--squares problems in an interior--point method for linear programming.
\newblock {Technical Report (in preparation)}, Department of Industrial
  Engineering and Management Sciences, Northwestern University, Evanston,
  IL~60208, USA, 1991.

\bibitem{ipm:Fourer2}
R.~Fourer and S.~Mehrotra.
\newblock Performance of an augmented system approach for solving
  least--squares problems in an interior--point method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:26--31, August 1991.

\bibitem{ipm:Fourer3}
R.~Fourer and S.~Mehrotra.
\newblock Solving symmetric indefinite systems in an interior--point method for
  linear programming.
\newblock {\em Mathematical Programming}, 62:15--39, 1993.

\bibitem{ipm:Fragniere1}
E.~Fragniere, J.~Gondzio, and R.Sarkissian.
\newblock Structure exploiting tool in algebraic modeling languages.
\newblock {Technical Report} 1997.2, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, June 1997.

\bibitem{ipm:Fragniere2}
E.~Fragniere, J.~Gondzio, and J.-Ph. Vial.
\newblock A planning model with one million scenarios solved on an affordable
  parallel machine.
\newblock {Logilab Technical Report} 1998.11, Department of Management Studies,
  University of Geneva, 102 Bd Carl Vogt, CH--1211 Geneva, Switzerland, June
  1998.

\bibitem{ipm:Fraley4}
C.~Fraley.
\newblock Computational aspects of some projective methods for linear
  programming.
\newblock {Working Paper}, COMIN, University of Geneva, 2~Rue de Candolle,
  CH--1211~Geneva~4, Switzerland, 1988.

\bibitem{ipm:Fraley1}
C.~Fraley.
\newblock Linear updates for a single\,--\,phase projective method.
\newblock {\em Operations Research Letters}, 9:169--174, 1990.

\bibitem{ipm:Fraley3}
C.~Fraley and J.-Ph. Vial.
\newblock Numerical study of projective methods for linear programming.
\newblock In S.~Dolecki, editor, {\em Optimization\,: Proceedings of the 5th
  French--German Conference in Castel--Novel, Varetz, France, October 1988},
  volume 1405 of {\em Lecture Notes in Mathematics}, pages 25--38. Springer
  Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Fraley2}
C.~Fraley and J.-Ph. Vial.
\newblock Single\,--\,phase versus multiple\,--\,phase projective methods for
  linear programming.
\newblock {Technical Report}, COMIN, University of Geneva, 2~Rue de Candolle,
  CH--1211~Geneva~4, Switzerland, 1989.

\bibitem{ipm:Fraley5}
C.~Fraley and J.-Ph. Vial.
\newblock Alternative approaches to feasibility in projective methods for
  linear programming.
\newblock {\em ORSA Journal on Computing}, 4:285--299, 1992.

\bibitem{ipm:Franklin1}
J.~Franklin.
\newblock Convergence in {Karmarkar's} algorithm for linear programming.
\newblock {\em SIAM Journal on Numerical Analysis}, 24:928--945, 1987.

\bibitem{ipm:Freedman2}
B.~A. Freedman, S.~C. Puthenpura, and L.~P. Sinha.
\newblock A new {Karmarkar}--based algorithm for optimizing convex, nonlinear
  functions with linear constraints.
\newblock {Technical Report}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733,
  USA, 1988.

\bibitem{ipm:Freedman1}
B.~A. Freedman, S.~C. Puthenpura, and L.~P. Sinha.
\newblock A new affine scaling based algorithm for optimizing convex, nonlinear
  functions with linear constraints.
\newblock {Technical Report}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733,
  USA, 1990.

\bibitem{ipm:Frenk1}
J.~B.~G. Frenk, J.~F. Sturm, and S.~Zhang.
\newblock An interior--point subgradient method for linearly constrained
  nondifferentiable convex programming.
\newblock {\em Optimization Methods and Software}, 10:197--215, 1998.

\bibitem{ipm:Freund1}
R.~M. Freund.
\newblock An analogous of {Karmarkar's} algorithm for inequality constrained
  linear programs, with a 'new' class of projective transformations for
  centering a polytope.
\newblock {\em Operations Research Letters}, 7:9--13, 1988.

\bibitem{ipm:Freund3}
R.~M. Freund.
\newblock A generalization/extension of {Karmarkar's} algorithm for inequality
  constrained linear programs based on projective centering of the polyhedra.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, April 1988.

\bibitem{ipm:Freund4}
R.~M. Freund.
\newblock Projective transformations for finding the w--center of a polyhedra.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, October 1988.

\bibitem{ipm:Freund22}
R.~M. Freund.
\newblock Projective transformations for interior point algorithms.
\newblock {Talk held at the AMS--ISM--SIAM Research Conference on
  ''Mathematical Developments Arising from Linear Programming'' in Bowdoin
  College, Brunswick, Maine, USA}, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, June 1988.

\bibitem{ipm:Freund5}
R.~M. Freund.
\newblock Projective transformations for interior point methods, {Part\,I\,:
  Basic} theory and linear programming.
\newblock {Working Paper} 2049--88, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, October 1988.

\bibitem{ipm:Freund6}
R.~M. Freund.
\newblock Projective transformations for interior point methods, {Part\,II\,:
  Analysis} of an algorithm for finding the weighted center of a polyhedral
  system.
\newblock {Working Paper} 2050--88, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, October 1988.

\bibitem{ipm:Freund17}
R.~M. Freund.
\newblock Projective transformations for interior point algorithms, a
  superlinearly convergent algorithm for the w--center problem.
\newblock {Working Paper}, Sloan School of Management, Massachusetts Institute
  of Technology, Cambridge, MA~02139, USA, 1989.
\newblock To appear in {\em Mathematical Programming}.

\bibitem{ipm:Freund10}
R.~M. Freund.
\newblock Interior point algorithms for solving a linear program directly from
  an infeasible 'warm start'.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, May 1990.

\bibitem{ipm:Freund12}
R.~M. Freund.
\newblock Newton's method for general parametric center problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, October 1990.

\bibitem{ipm:Freund11}
R.~M. Freund.
\newblock Recent results and perspectives on solving linear programming from an
  infeasible 'warm start'.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, Sloan
  School of Management, Massachusetts Institute of Technology, Cambridge,
  MA~02139, USA, July 1990.

\bibitem{ipm:Freund9}
R.~M. Freund.
\newblock Theoretical efficiency of solving a linear program from an infeasible
  'warm start'.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Sloan School of Management, Massachusetts Institute of
  Technology, Cambridge, MA~02139, USA, January 1990.

\bibitem{ipm:Freund24}
R.~M. Freund.
\newblock Algorithms for solving a linear program from infeasible warm start
  based on the intuitive geometrics of {LP}.
\newblock {Talk held at the 14th International Mathematical Programming
  Symposium in Amsterdam, The Netherlands}, Sloan School of Management,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, August 1991.

\bibitem{ipm:Freund18}
R.~M. Freund.
\newblock A combined {phase\,I\,--\,phase\,II} algorithm for {LP} based on the
  intuitive geometry of linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, November 1991.

\bibitem{ipm:Freund23}
R.~M. Freund.
\newblock Computational complexity of tracing the path of centers of a linear
  inequality system as the data for the system is parametrically deformed.
\newblock {Talk held at the Workshop on Complexity Issues for Numerical
  Optimization, Cornell University, Ithaca, NY, USA}, Sloan School of
  Management, Massachusetts Institute of Technology, Cambridge, MA~02139, USA,
  March 1991.

\bibitem{ipm:Freund16}
R.~M. Freund.
\newblock Interior--point methods for linear programming\,: {A} status report.
\newblock {Tutorial held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Sloan School of Management, Massachusetts Institute of
  Technology, Cambridge, MA~02139, USA, May 1991.

\bibitem{ipm:Freund2}
R.~M. Freund.
\newblock Polynomial--time algorithms for linear programming based only on
  primal scaling and projected gradients of a potential function.
\newblock {\em Mathematical Programming}, 51:203--222, 1991.

\bibitem{ipm:Freund8}
R.~M. Freund.
\newblock A potential--function reduction algorithm for solving a linear
  program directly from an infeasible 'warm start'.
\newblock {\em Mathematical Programming}, 52:441--466, 1991.

\bibitem{ipm:Freund25}
R.~M. Freund.
\newblock Solving a linear program from an infeasible warm start\,:
  {Conceptual} issues, theory, and a new interior point algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, November 1991.

\bibitem{ipm:Freund7}
R.~M. Freund.
\newblock Theoretical efficiency of a shifted barrier function algorithm for
  linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:19--41, 1991.

\bibitem{ipm:Freund26}
R.~M. Freund.
\newblock Following a trajectory from an infeasible point to an optimal linear
  programming solution.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, May 1992.

\bibitem{ipm:Freund19}
R.~M. Freund.
\newblock Pre--selection of the {phase\,I\,--\,phase\,II} balance in a
  path--following algorithm for the 'warm start' linear programming problem.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, May 1992.

\bibitem{ipm:Freund28}
R.~M. Freund.
\newblock Projective transformations for interior--point algorithms, and a
  superlinearly convergent algorithm for the w--center problem.
\newblock {\em Mathematical Programming}, 58:385--414, 1993.
\newblock Amalgamation of Freund \cite{ipm:Freund5,ipm:Freund6}.

\bibitem{ipm:Freund30}
R.~M. Freund.
\newblock Complexity of an algorithm for finding an approximate solution of a
  semi--definite program, with no regularity condition.
\newblock {Working Paper} OR--302--94, Operations Research Center,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, 1994.

\bibitem{ipm:Freund20}
R.~M. Freund.
\newblock A potential reduction algorithm with user--specified
  {phase\,I\,---\,phase\,II} balance for solving a linear program from an
  infeasible warm start.
\newblock {\em SIAM Journal on Optimization}, 5:247--268, 1995.

\bibitem{ipm:Freund29}
R.~M. Freund.
\newblock An infeasible--start algorithm for linear programming whose
  complexity depends on the distance from the starting point to the optimal
  solution.
\newblock {\em Annals of Operations Research}, 62:29--57, 1996.

\bibitem{ipm:Freund35}
R.~M. Freund and S.~Mizuno.
\newblock Interior point methods\,: {Current} status and future directions.
\newblock {\em Optima (The Mathematical Programming Society Newsletter)},
  51:1--9, 1996.

\bibitem{ipm:Freund33}
R.~M. Freund and M.~A. Nunez.
\newblock Condition measures and properties of the central trajectory of a
  linear program.
\newblock {Sloan Working Paper}, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, March 1996.
\newblock Submitted to {\em Mathematical Programming}. Identical version to
  Nunez and Freund \cite{ipm:Nunez2}.

\bibitem{ipm:Freund14}
R.~M. Freund and K.~C. Tan.
\newblock A parametric center algorithm and a strictly monotonic central path
  algorithm for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, October 1989.

\bibitem{ipm:Freund15}
R.~M. Freund and K.~C. Tan.
\newblock Newton's method for parametric center problems.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, Sloan
  School of Management, Massachusetts Institute of Technology, Cambridge,
  MA~02139, USA, July 1990.

\bibitem{ipm:Freund21}
R.~M. Freund and K.~C. Tan.
\newblock Newton's method for the general parametric centering problem with
  applications.
\newblock {Working Paper}, Sloan School of Management, Massachusetts Institute
  of Technology, Cambridge, MA~02139, USA, 1990.
\newblock To appear in {\em Mathematical Programming}.

\bibitem{ipm:Freund13}
R.~M. Freund and K.~C. Tan.
\newblock A method for the parametric center problem, with a strictly monotone
  polynomial--time algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):775--801, 1991.

\bibitem{ipm:Freund27}
R.~M. Freund and M.~J. Todd.
\newblock Barrier functions and interior--point algorithms for linear
  programming with zero--, one--, or two--sided bounds of the variables.
\newblock {\em Mathematics of Operations Research}, 20:415--440, 1995.

\bibitem{ipm:Freund36}
R.~M. Freund and J.~Vera.
\newblock Condition--based complexity of convex optimization in conic linear
  form via the ellipsoid algorithm.
\newblock {Technical Report}, Operations Research Center, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, September 1997.

\bibitem{ipm:Freund32}
R.~M. Freund and J.~R. Vera.
\newblock Some characterizations and properties of the distance to
  ill--posedness and the condition measure of a conic linear system.
\newblock {Sloan Working Paper} 3862--95--MSA, Sloan School of Management,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, November
  1995.
\newblock Submitted to {\em Mathematical Programming}.

\bibitem{ipm:Freund31}
R.~M. Freund and H.~K. Wadhwa.
\newblock Implementation and empirical study of a combined
  {phase\,I\,--\,phase\,II} potential reduction algorithm for linear
  programming.
\newblock {Working Paper} 3411--92, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, March 1992.

\bibitem{ipm:RFreund1}
R.~W. Freund and F.~Jarre.
\newblock An interior--point method for convex fractional programming.
\newblock {AT \& T Numerical Analysis Manuscript} 93--03, AT{\&}T Bell
  Laboratories, Murray Hill, NJ~07974, USA, May 1993.

\bibitem{ipm:RFreund3}
R.~W. Freund and F.~Jarre.
\newblock On the complexity of convex fractional programs.
\newblock {Technical Report (in preparation)}, AT{\&}T Bell Laboratories,
  Murray Hill, NJ~07974, USA, 1993.

\bibitem{ipm:RFreund4}
R.~W. Freund and F.~Jarre.
\newblock An interior--point method for fractional programs with convex
  constraints.
\newblock {\em Mathematical Programming}, pages 407--440, 1994.
\newblock See also {\em Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik
  74(1994), T523--T525}.

\bibitem{ipm:RFreund2}
R.~W. Freund and F.~Jarre.
\newblock An interior--point method for multi--fractional programming with
  convex constraints.
\newblock {\em Journal of Optimization Theory and Applications}, 85:125--161,
  1995.

\bibitem{ipm:RFreund6}
R.~W. Freund and F.~Jarre.
\newblock A {QMR}--based interior--point algorithm for solving linear programs.
\newblock {\em Mathematical Programming}, 76:183--210, 1997.

\bibitem{ipm:RFreund8}
R.~W. Freund, F.~Jarre, and S.~Mizuno.
\newblock Convergence of a class of inexact interior--point algorithms for
  linear program.
\newblock {Numerical Analysis Manuscript} 97--3--11, AT{\&}T Bell Laboratories,
  Murray Hill, NJ~07974, USA, October 1997.

\bibitem{ipm:RFreund5}
R.~W. Freund, F.~Jarre, and S.~Schaible.
\newblock On interior--point methods for fractional programs and their convex
  reformulation.
\newblock {AT \& T Numerical Analysis Manuscript} 94--17, AT{\&}T Bell
  Laboratories, Murray Hill, NJ~07974, USA, 1994.

\bibitem{ipm:RFreund7}
R.~W. Freund, F.~Jarre, and S.~Schaible.
\newblock On self--concordant barrier functions for conic hulls and fractional
  programming.
\newblock {\em Mathematical Programming}, 74:237--246, 1996.

\bibitem{ipm:Fricker1}
F.~Fricker.
\newblock {Komplexe Optimierungsaufgaben schneller l{\"o}sen~(Solving complex
  optimization problems faster)}.
\newblock {\em Frankfurter Allgemeine Zeitung, Sektion\,: Natur und Wissen},
  March 27, 1985.
\newblock (In German).

\bibitem{ipm:Frisch3}
K.~R. Frisch.
\newblock Principles of linear programming---{With} a particular reference to
  the double gradient form of the logarithmic potential method.
\newblock Memorandum, Institute of Economics, University of Oslo, Oslo, Norway,
  October 1954.

\bibitem{ipm:Frisch5}
K.~R. Frisch.
\newblock Principles of linear programming--the double gradient form of the
  logarithmic potential method.
\newblock Memorandum, Institute of Economics, University of Oslo, Oslo, Norway,
  October 1954.

\bibitem{ipm:Frisch1}
K.~R. Frisch.
\newblock The logarithmic potential method for convex programming.
\newblock Unpublished manuscript, Institute of Economics, University of Oslo,
  Oslo, Norway, May 1955.

\bibitem{ipm:Frisch6}
K.~R. Frisch.
\newblock La resolution des problemes de programme lineaire par la methode du
  potential logarithmique.
\newblock {\em Cahiers du Seminaire D'Econometrie}, 4:7--20, 1956.

\bibitem{ipm:Frisch4}
K.~R. Frisch.
\newblock Linear dependencies and a mechanized form of the multiplex method for
  linear programming.
\newblock Memorandum, Institute of Economics, University of Oslo, Oslo, Norway,
  1957.

\bibitem{ipm:Frisch2}
K.~R. Frisch.
\newblock The multiplex method for linear programming.
\newblock {\em Sankhya}, 18:329--362, 1957.

\bibitem{ipm:Fu1}
M.~Fu, Z.-Q. Luo, and Y.~Ye.
\newblock Approximation algorithms for quadratic programming.
\newblock {\em Journal of Combinatorial Optimization}, 2:29--50, 1998.

\bibitem{ipm:Fujie1}
T.~Fujie and M.~Kojima.
\newblock Semidefinite programming relaxation for nonconvex quadratic programs.
\newblock {\em Journal of Global Optimization}, 10:367--380, 1997.

\bibitem{ipm:Fujisawa5}
K.~Fujisawa.
\newblock Numerical experiments on interior point method programs related to
  positive semidefinite programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
  1004:190--199, 1997.
\newblock (In Japanese, English summary).

\bibitem{ipm:Fujisawa4}
K.~Fujisawa, M.~Fukuda, M.~Kojima, and K.~Nakata.
\newblock Numerical evaluation of {SDPA (SemiDefinite Programming Algorithm)}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--330, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan,
  September 1997.

\bibitem{ipm:Fujisawa2}
K.~Fujisawa and M.~Kojima.
\newblock {SDPA (Semi--Definite Programming Algorithm) --- The Software}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research}, Department of Information Sciences, Tokyo Institute of Technology,
  Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, November 1995.

\bibitem{ipm:Fujisawa1}
K.~Fujisawa and M.~Kojima.
\newblock {SDPA (Semi--Definite Programming Algorithm) --- User's Manual}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--308, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, November 1995.
\newblock Revised August 1996.

\bibitem{ipm:Fujisawa3}
K.~Fujisawa, M.~Kojima, and K.~Nakata.
\newblock Exploiting sparsity in primal--dual interior--point methods for
  semidefinite programming.
\newblock {\em Mathematical Programming}, 78:235--253, 1997.

\bibitem{ipm:Fukushima1}
M.~Fukushima, N.~Arai, and T.~Ibaraki.
\newblock An interior method for nonlinear minimum cost network flow problems.
\newblock {\em Systems and Control (Japan)}, 31(11):837--843, 1987.

\bibitem{ipm:Gahinet1}
P.~Gahinet and A.~S. Nemirovsky.
\newblock The projective method for solving linear matrix inequalities.
\newblock {\em Mathematical Programming}, 77:163--190, 1997.
\newblock See also Nemirovsky and Gahinet \cite{ipm:Nemirovsky5}.

\bibitem{ipm:Garcia1}
C.~B. Garcia and F.~J. Gould.
\newblock An application of homotopy to solving linear programs.
\newblock {\em Mathematical Programming}, 27:263--282, 1983.

\bibitem{ipm:Garey1}
M.~R. Garey and D.~M. Gay.
\newblock Letter from the {AT~\&~T Laboratories}.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, December 1985.

\bibitem{ipm:Garfunkel1}
S.~A. Garfunkel, L.~A. Steen, and J.~Malkevitch.
\newblock {\em For All Practical Purposes\,: Introduction to Contemporary
  Mathematics}, chapter 4\,: {L}inear programming\,: {A}n alternative to the
  simplex method, pages 80--83, 362.
\newblock W. H. Freeman and Company, New York, 1988.

\bibitem{ipm:Garzillo1}
A.~Garzillo, M.~Innorta, and M.~Ricci.
\newblock The problem of active and reactive optimum power dispatching solving
  by utilizing a primal--dual interior point method.
\newblock {\em Energia Elettrica}, 74:113--122, 1997.

\bibitem{ipm:Gassmann1}
H.~I. Gassmann.
\newblock Interior point methods in stochastic linear programming\,: {Reducing}
  fill--in.
\newblock {Working Paper} WP--91--4, Dalhousie School of Business
  Administration, Dalhousie University, Halifax, Canada~B3H\,1Z5, 1991.
\newblock Available through\,: http://ttg.sba.dal.ca/sba/doc/fillin.ps or
  http://ttg.sba.dal.ca/sba/profs/hgassmann/fillin.html.

\bibitem{ipm:Gay1}
D.~M. Gay.
\newblock Sparse projections in {Karmarkar's} linear programming algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA,
  USA}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, November 1985.
\newblock No underlying report.

\bibitem{ipm:Gay2}
D.~M. Gay.
\newblock Pictures of {Karmarkar's} linear programming algorithm.
\newblock {Computer Science Technical Report} 136, AT~\&~T~Bell Laboratories,
  Murray Hill, NJ~07974, USA, January 1987.

\bibitem{ipm:Gay3}
D.~M. Gay.
\newblock A variant of {Karmarkar's} linear programming algorithm for problems
  in standard form.
\newblock {\em Mathematical Programming}, 37:81--90, 1987.
\newblock Errata in {\em Mathematical Programming}, 40:111, 1988.

\bibitem{ipm:Gay4}
D.~M. Gay.
\newblock Massive memory buys little speed for complete, in--core sparse
  {C}holesky factorizations on some scalar computers.
\newblock {\em Linear Algebra and Its Applications}, 152:291--314, 1991.

\bibitem{ipm:Gay5}
D.~M. Gay.
\newblock Stopping tests that compute optimal solutions for interior--point
  linear programming algorithms.
\newblock In S.~Gomez, J.~P. Hennart, and R.~A. Tapia, editors, {\em Advances
  in Numerical Partial Differential Equations and Optimization\,: Proceedings
  of the Fifth Mexico--United States Workshop}, volume~47 of {\em Proceedings
  in Applied Mathematics}, pages 17--42. SIAM Publications, Philadelphia, PA,
  USA, 1991.

\bibitem{ipm:Gay6}
D.~M. Gay, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock The {Karmarkar} algorithm\,: {Adding} wings to linear programming.
\newblock {\em Record AT~\&~T~Bell Laboratories}, 64(2):4--10, 1986.

\bibitem{ipm:Gay7}
D.~M. Gay, M.~Kojima, and R.~A. Tapia.
\newblock {\em Interior Point Methods for Linear Programming}, volume 152 of
  {\em Linear Algebra and Its Applications}.
\newblock North Holland, Amsterdam, The Netherlands, July 1991.
\newblock (Special issue).

\bibitem{ipm:Gay8}
D.~M. Gay, M.~L. Overton, and M.~H. Wright.
\newblock Primal--dual interior point methods for indefinite nonlinear
  programming.
\newblock {Technical Report}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974,
  USA, 1995.
\newblock (In preparation).

\bibitem{ipm:Gay9}
D.~M. Gay, M.~L. Overton, and M.~H. Wright.
\newblock A primal--dual interior point method for nonconvex nonlinear
  programming.
\newblock {Technical Report} 97--4--08, AT~\&~T~Bell Laboratories, Murray Hill,
  NJ~07974, USA, July 1997.
\newblock To appear in {\em{Advances in Nonlinear Programming, Y. Yuan (ed.),
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998}}.

\bibitem{ipm:Ge1}
R.~Ge.
\newblock Solving linear programming problems via linear minimax problems.
\newblock {\em Applied Mathematics and Computation}, 46(1):59--77, 1991.

\bibitem{ipm:Gelbaum1}
B.~R. Gelbaum.
\newblock {\em Linear Algebra\,: Basics, Practice and Theory}, chapter 5.7~:
  {The Karmarkar algorithm}, pages 504--527.
\newblock North Holland, New York, 1989.

\bibitem{ipm:Ghare1}
P.~Ghare.
\newblock Free decision variables and simplified interior point methods for
  linear programming.
\newblock {Talk held at the Symposium APMOD\,'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Northern Virginia Graduate Centre, USA, January 1991.

\bibitem{ipm:Ghellinck1}
{G. de} Ghellinck and J.-Ph. Vial.
\newblock A polynomial {N}ewton method for linear programming.
\newblock {\em Algorithmica}, 1(4):425--453, 1986.

\bibitem{ipm:Ghellinck2}
{G. de} Ghellinck and J.-Ph. Vial.
\newblock An extension of {Karmarkar's} algorithm for solving a system of
  linear homogeneous equations on the simplex.
\newblock {\em Mathematical Programming}, 39:79--92, 1987.

\bibitem{ipm:Ghellinck3}
{G. de} Ghellinck and J.-Ph. Vial.
\newblock A unified approach to projective and affine algorithms for linear
  programming.
\newblock {Talk held at the EURO/TIMS Joint International Conference on
  Operational Research in Paris, France}, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, July 1988.

\bibitem{ipm:Gill6}
P.~E. Gill, A.~Marxen, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock Solution of the primal {LP}-problem by a barrier method\,: {S}ome
  implementation aspects.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Systems Optimization Laboratory, Department of Operations Research,
  Stanford University, Stanford, CA~94305, USA, April 1988.
\newblock See Marxen \cite{ipm:Marxen1,ipm:Marxen2}.

\bibitem{ipm:Gill9}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Solving reduced {KKT}--systems in barrier methods for linear and
  quadratic programming.
\newblock {Technical Report} SOL~91-7, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, July 1991.
\newblock See also Gill et al. \cite{ipm:Gill12}.

\bibitem{ipm:Gill11}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Preconditioners for indefinite systems arising in optimization.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 13:292--311,
  1992.

\bibitem{ipm:Gill12}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Solving reduced {KKT}--systems in barrier methods for linear
  programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
  1993}, volume 303 of {\em Pitman Research Notes in Mathematics}, pages
  89--104. Longman Scientific \& Technical, Harlow, United Kingdom, 1994.
\newblock See also Gill et al. \cite{ipm:Gill9}.

\bibitem{ipm:Gill8}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Primal--dual methods for linear programming.
\newblock {\em Mathematical Programming}, 70:251--277, 1995.

\bibitem{ipm:Gill2}
P.~E. Gill, W.~Murray, and M.~A. Saunders.
\newblock Interior--point methods for linear programs\,: {A} challenge to the
  simplex method.
\newblock {Technical Report} SOL~88--14, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, July 1988.

\bibitem{ipm:Gill1}
P.~E. Gill, W.~Murray, and M.~A. Saunders.
\newblock A single\,--\,phase dual barrier method for linear programming.
\newblock {Technical Report} SOL~88--10, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, August 1988.

\bibitem{ipm:Gill7}
P.~E. Gill, W.~Murray, M.~A. Saunders, J.~A. Tomlin, and M.~H. Wright.
\newblock On projected {Newton} barrier methods for linear programming and an
  equivalence to {Karmarkar's} projective method.
\newblock {\em Mathematical Programming}, 36:183--209, 1986.

\bibitem{ipm:Gill3}
P.~E. Gill, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock A note on nonlinear approaches to linear programming.
\newblock {Technical Report} SOL~86--7, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, April 1986.

\bibitem{ipm:Gill4}
P.~E. Gill, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock Convergence results for a shifted barrier linear programming method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Systems Optimization Laboratory, Department of Operations Research,
  Stanford University, Stanford, CA~94305, USA, April 1988.

\bibitem{ipm:Gill5}
P.~E. Gill, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock Shifted barrier methods for linear programming.
\newblock {Technical Report} SOL~88--9, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, August 1988.

\bibitem{ipm:Gill10}
P.~E. Gill, W.~Murray, and M.~H. Wright.
\newblock {\em Numerical Linear Algebra and Optimization, {V}ol.\,2}.
\newblock Addison Wesley Publishing Company, Amsterdam, The Netherlands, 1992.
\newblock Chapter on interior point methods.

\bibitem{ipm:Gill13}
P.~E. Gill, M.~A. Saunders, and J.~R. Shinnerl.
\newblock On the stability of {Cholesky} factorization for symmetric
  quasidefinite systems.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 17:35--46,
  1996.

\bibitem{ipm:Glassman1}
N.~D. Glassman.
\newblock {ONR (Office of Naval Research)} focuses on interior methods.
\newblock {\em SIAM News}, 20(2):12, March 1987.

\bibitem{ipm:Gleick1}
J.~Gleick.
\newblock Breakthrough in problem solving.
\newblock {\em The New York Times}, November 19, 1984.

\bibitem{ipm:Goessl1}
H.~Goessl.
\newblock {Eine Modifikation des Verfahrens von Karmarkar basierend auf einer
  Formulierung des Algorithmus im Originalproblem~(A modification of
  Karmarkar's algorithm based on a formulation of the algorithm in the original
  problem)}.
\newblock {Interner Bericht der intergrierten Arbeitsgruppe Mathematische
  Probleme aus dem Ingenieurbereich}, Fachbereich Mathematik, Gesamthochschule
  Wuppertal, D--42097~Wuppertal~1, Germany, October 1986.
\newblock (In German).

\bibitem{ipm:Goessl2}
H.~Goessl.
\newblock {Eine Verallgemeinerung und eine duale Variante des Verfahrens von de
  Ghellinck und Vial zur linearen Optimierung~(A generalization and a dual
  variant of the algorithm of de Ghellinck and Vial for linear programming)}.
\newblock {Interner Bericht der intergrierten Arbeitsgruppe Mathematische
  Probleme aus dem Ingenieurbereich}, Fachbereich Mathematik, Gesamthochschule
  Wuppertal, D--42097~Wuppertal~1, Germany, December 1987.
\newblock (In German).

\bibitem{ipm:Goessl3}
H.~Goessl.
\newblock {\em {Varianten der polynomialen Newtonmethode zur linearen
  Optimierung~(Variants of the polynomial Newton method for linear
  programming)}}.
\newblock PhD thesis, Fachbereich Mathematik, Gesamthochschule Wuppertal,
  D--42097~Wuppertal~1, Germany, 1989.
\newblock (In German).

\bibitem{ipm:Goffin8}
J.-L. Goffin.
\newblock Affine methods in nondifferentiable optimization.
\newblock {CORE Discussion Paper} 8744, Center for Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348 Louvain--la--Neuve,
  Belgium, 1987.

\bibitem{ipm:Goffin1}
J.-L. Goffin.
\newblock Affine and projective methods in nondifferentiable optimization.
\newblock In K.~H. Hoffmann, J.~B. Hiriat-Urruty, C.~Lemarechal, and J.~Zowe,
  editors, {\em Trends in Mathematical Optimization\,: Proceedings of the 4th
  French--German Conference on Optimization in Irsee, Germany, April 1986},
  volume~84 of {\em International Series of Numerical Mathematics}, pages
  79--91. Birkh{\"a}user Verlag, Basel, Switzerland, 1988.

\bibitem{ipm:Goffin2}
J.-L. Goffin.
\newblock Decomposition and large scale optimization with the interior point
  algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Faculty of Management, McGill University, Montreal, Ontario,
  Canada, October 1990.

\bibitem{ipm:Goffin16}
J.-L. Goffin.
\newblock Using the primal dual infeasible {Newton} method in the analytic
  center method for problems defined by deep cutting planes.
\newblock {Technical Report}, Faculty of Management, McGill University,
  Montreal, Ontario, Canada, September 1994.

\bibitem{ipm:Goffin13}
J.-L. Goffin, J.~Gondzio, R.~Sarkissian, and J.-Ph. Vial.
\newblock Solving nonlinear multicommodity flow problems by the analytic center
  cutting plane method.
\newblock {\em Mathematical Programming}, 76:131--154, 1997.

\bibitem{ipm:Goffin4}
J.-L. Goffin, A.~Haurie, and J.-Ph. Vial.
\newblock Decomposition and nondifferentiable optimization with the projective
  algorithm.
\newblock {\em Management Science}, 38(2):284--302, 1992.

\bibitem{ipm:Goffin7}
J.-L. Goffin, A.~Haurie, J.-Ph. Vial, and D.~L. Zhu.
\newblock Using central prices in the decomposition of linear programs.
\newblock {\em European Journal of Operational Research}, 64:393--409, 1993.

\bibitem{ipm:Goffin15}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock Further complexity analysis of a primal--dual column generation
  algorithm for convex or quasiconvex feasibility problems.
\newblock {Technical Report}, Faculty of Management, McGill University,
  Montreal, Ontario, Canada, August 1993.
\newblock To appear in {\em SIAM Journal on Optimization}.

\bibitem{ipm:Goffin14}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock Complexity analysis of a potential reduction and column generation
  algorithm for convex programming.
\newblock {Technical Report}, Faculty of Management, McGill University,
  Montreal, Ontario, Canada, 1994.
\newblock To appear in {\em SIAM Journal on Optimization}.

\bibitem{ipm:Goffin11}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock On the complexity of a column generation algorithm for convex or
  quasiconvex feasibility problems.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 182--191.
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Goffin12}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock Complexity analysis of an interior cutting plane method for convex
  feasibility problems.
\newblock {\em SIAM Journal on Optimization}, 6:638--652, 1996.

\bibitem{ipm:Goffin17}
J.-L. Goffin, P.~Marcotte, and D.~Zhu.
\newblock An analytic center cutting plane method for pseudomonotone
  variational inequalities.
\newblock {\em Operations Research Letters}, 20:1--6, 1997.

\bibitem{ipm:Goffin18}
J.-L. Goffin and F.~Sharifi-Mokhtarian-Mokhtarian.
\newblock Using the primal dual infeasible {Newton} method in the analytic
  center method for problems defined by deep cutting planes.
\newblock {Technical Report} GERAD G--94--41, Faculty of Management, McGill
  University, Montreal, Ontario, Canada, 1994.
\newblock Revised April 1996.

\bibitem{ipm:Goffin10}
J.-L. Goffin and J.-Ph. Vial.
\newblock On the computation of weighted analytic centers and dual ellipsoids
  with the projective algorithm.
\newblock {Manuscript}, Faculte des Sciences Economiques et Sociales,
  Universite de Geneve, Geneve, Suisse, July 1989.

\bibitem{ipm:Goffin3}
J.-L. Goffin and J.-Ph. Vial.
\newblock Cutting planes and column generation techniques with the projective
  algorithm.
\newblock {\em Journal of Optimization Theory and Applications}, 65:409--429,
  1990.

\bibitem{ipm:Goffin9}
J.-L. Goffin and J.-Ph. Vial.
\newblock Experimentation with the interior cutting plane method {(ICPM)}.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Faculty of Management, McGill University, Montreal, Ontario,
  Canada, May 1992.

\bibitem{ipm:Goffin6}
J.-L. Goffin and J.-Ph. Vial.
\newblock On the computation of weighted analytic centers and dual ellipsoids
  with the projective algorithm.
\newblock {\em Mathematical Programming}, 60:81--92, 1993.

\bibitem{ipm:Goffin5}
J.-L. Goffin and J.-Ph. Vial.
\newblock Short steps with {Karmarkar's} projective algorithm for linear
  programming.
\newblock {\em SIAM Journal on Optimization}, 4:193--207, 1994.

\bibitem{ipm:Goffin20}
J.-L. Goffin and J.-Ph. Vial.
\newblock A two--cut approach in the analytic center cutting plane method.
\newblock {Logilab Technical Report} 97.6, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva, Switzerland,
  August 1997.

\bibitem{ipm:Goffin21}
J.-L. Goffin and J.-Ph. Vial.
\newblock Multiple cuts in the analytic center cutting plane method.
\newblock {Logilab Technical Report} 98.10, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, 102~Bd Carl Vogt, CH--1211 Geneva,
  Switzerland, June 1998.

\bibitem{ipm:Goffin19}
J.-L. Goffin and J.-Ph. Vial.
\newblock Shallow, deep and very deep cuts in the analytic center cutting plane
  method.
\newblock {\em Mathematical Programming}, 84:89--103, 1999.

\bibitem{ipm:Goldberg1}
A.~V. Goldberg, S.~A. Plotkin, D.~B. Shmoys, and E.~Tardos.
\newblock Interior--point methods in parallel computation.
\newblock In {\em Proceedings of the 30th Annual Symposium on Foundations of
  Computer Science, Research Triangle Park, NC, USA, 1989}, pages 350--355.
  IEEE Computer Society Press, Los Alamitos, CA, USA, 1990.

\bibitem{ipm:Goldberg2}
A.~V. Goldberg, S.~A Plotkin, D.~B. Shmoys, and E.~Tardos.
\newblock Using interior--point methods for fast parallel algorithms for
  bipartite matching and related problems.
\newblock {\em SIAM Journal on Computing}, 21(1):140--150, 1992.

\bibitem{ipm:Goldfarb1}
D.~Goldfarb.
\newblock A relaxed version of {Karmarkar's} method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
  FL, USA}, Department of Industrial Engineering and Operations Research,
  Columbia University, New York, NY~10027, USA, October 1986.

\bibitem{ipm:Goldfarb2}
D.~Goldfarb.
\newblock A primal projective interior point method for linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Department of Industrial Engineering and Operations Research,
  Columbia University, New York, NY~10027, USA, January 1990.

\bibitem{ipm:Goldfarb10}
D.~Goldfarb and S.~Liu.
\newblock Interior point potential function reduction algorithm for solving
  convex quadratic programming.
\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, 1990.

\bibitem{ipm:Goldfarb3}
D.~Goldfarb and S.~Liu.
\newblock An ${O(n^{3}L)}$ primal interior point algorithm for convex quadratic
  programming.
\newblock {\em Mathematical Programming}, 49:325--340, 1990/91.

\bibitem{ipm:Goldfarb12}
D.~Goldfarb and S.~Liu.
\newblock An {$O(n^{3}L)$} primal--dual potential reduction algorithm for
  solving quadratic programs.
\newblock {\em Mathematical Programming}, 61:161--170, 1993.

\bibitem{ipm:Goldfarb9}
D.~Goldfarb, S.~Liu, and S.~Wang.
\newblock A logarithmic barrier function algorithm for quadratically
  constrained convex programming.
\newblock {\em SIAM Journal on Optimization}, 1:252--267, 1991.

\bibitem{ipm:Goldfarb6}
D.~Goldfarb and S.~Mehrotra.
\newblock A homogeneous equations variant of {Karmarkar's} algorithm for
  solving linear programs.
\newblock {Talk held at ORSA/TIMS Joint National Meeting in New Orleans, USA},
  Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, May 1987.

\bibitem{ipm:Goldfarb5}
D.~Goldfarb and S.~Mehrotra.
\newblock Relaxed variants of {Karmarkar's} algorithm for linear programs with
  unknown optimal objective value.
\newblock {\em Mathematical Programming}, 40:183--195, 1988.

\bibitem{ipm:Goldfarb4}
D.~Goldfarb and S.~Mehrotra.
\newblock A relaxed version of {Karmarkar's} method.
\newblock {\em Mathematical Programming}, 40:289--315, 1988.

\bibitem{ipm:Goldfarb7}
D.~Goldfarb and S.~Mehrotra.
\newblock A self--correcting version of {Karmarkar's} algorithm.
\newblock {\em SIAM Journal on Numerical Analysis}, 26:1006--1015, 1989.

\bibitem{ipm:Goldfarb15}
D.~Goldfarb and K.~Scheinberg.
\newblock Interior point trajectories in semidefinite programs.
\newblock {\em SIAM Journal on Optimization}, 8:871--886, 1998.

\bibitem{ipm:Goldfarb13}
D.~Goldfarb and D.~X. Shaw.
\newblock A path--following projective interior point method for linear
  programming.
\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, 1991.
\newblock To appear in {\em SIAM Journal on Optimization}.

\bibitem{ipm:Goldfarb14}
D.~Goldfarb and D.~X. Shaw.
\newblock On the complexity of a class of projective interior point methods.
\newblock {\em Mathematics of Operations Research}, 20:116--134, 1995.

\bibitem{ipm:Goldfarb8}
D.~Goldfarb and M.~J. Todd.
\newblock {Linear Programming}.
\newblock In G.~L. Nemhauser, A.~H.~G. {Rinnooy Kan}, and M.~J. Todd, editors,
  {\em Optimization}, volume~1 of {\em Handbooks in Operations Research and
  Management Science}, pages 141--170. North Holland, Amsterdam, The
  Netherlands, 1989.

\bibitem{ipm:Goldfarb11}
D.~Goldfarb and D.~Xiao.
\newblock A primal projective interior point method for linear programming.
\newblock {\em Mathematical Programming}, 51:17--43, 1991.

\bibitem{ipm:Golshtejn1}
E.~G. Gol'shtejn, A.~S. Nemirovsky, and Yu.~E. Nesterov.
\newblock On some recent advances in optimization.
\newblock {\em Ekonomika i Matematickeskie Metody (Moscow)}, 26(1):178--190,
  1990.
\newblock (In Russian).

\bibitem{ipm:Gondzio2}
J.~Gondzio.
\newblock An advanced implementation of {Cholesky} factorization for computing
  projections in interior point methods for large scale linear programming.
\newblock Cahier 107, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, December 1991.
\newblock Published in Gondzio\,\cite{ipm:Gondzio4} after title change.

\bibitem{ipm:Gondzio1}
J.~Gondzio.
\newblock Splitting dense columns of constraint matrix in interior point
  methods for large scale linear programming.
\newblock {\em Optimization}, 24:285--297, 1992.

\bibitem{ipm:Gondzio4}
J.~Gondzio.
\newblock Implementing {Cholesky} factorization for interior point methods of
  linear programming.
\newblock {\em Optimization}, 27:121--140, 1993.
\newblock Title change version of Gondzio\,\cite{ipm:Gondzio2}.

\bibitem{ipm:Gondzio11}
J.~Gondzio.
\newblock Preconditioned conjugate gradients in an interior point method for
  two--stage stochastic programming.
\newblock {Working Paper} WP--94--130, IIASA International Institute for
  Applied Systems Analysis, A--2361~Laxenburg, Austria, 1994.

\bibitem{ipm:Gondzio9}
J.~Gondzio.
\newblock {HOPDM (Version2.12) -- A fast LP} solver based on a primal--dual
  interior point method.
\newblock {\em European Journal of Operational Research}, 85:221--225, 1995.
\newblock See also Altman and Gondzio \cite{ipm:Altman3}.

\bibitem{ipm:Gondzio10}
J.~Gondzio.
\newblock On the use of multiple centrality corrections in a primal--dual
  method for large scale linear programming.
\newblock {\em International Symposium of Economic Informatics (Bucharest,
  Romania, May 1995)}, pages 311--321, 1995.
\newblock See also Gondzio \cite{ipm:Gondzio8}.

\bibitem{ipm:Gondzio8}
J.~Gondzio.
\newblock Multiple centrality corrections in a primal--dual method for linear
  programming.
\newblock {\em Computational Optimization and Applications}, 6:137--156, 1996.
\newblock See also Gondzio \cite{ipm:Gondzio10}.

\bibitem{ipm:Gondzio5}
J.~Gondzio.
\newblock Presolve analysis of linear programs prior to applying the
  interior--point method.
\newblock {\em INFORMS Journal on Computing}, 9:73--91, 1997.

\bibitem{ipm:Gondzio17}
J.~Gondzio.
\newblock Warm start of the priml--dual method applied in the cutting plane
  scheme.
\newblock {\em Mathematical Programming}, 83:125--143, 1998.

\bibitem{ipm:Gondzio12}
J.~Gondzio and M.~Makowski.
\newblock {HOPDM--Modular solver for LP problems user's guide to version\,
  2.12}.
\newblock {Working Paper} WP--95--50, IIASA International Institute for Applied
  Systems Analysis, A--2361~Laxenburg, Austria, June 1995.

\bibitem{ipm:Gondzio6}
J.~Gondzio and M.~Makowski.
\newblock Solving a class of {LP} problems with a primal--dual logarithmic
  barrier method.
\newblock {\em European Journal of Operational Research}, 80:184--192, 1995.

\bibitem{ipm:Gondzio13}
J.~Gondzio and {O. du} Merle.
\newblock Analytic center cutting plane method -- {User's} guide for the
  library.
\newblock {Technical Report} 1995.33, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, December 1995.

\bibitem{ipm:Gondzio14}
J.~Gondzio, {O. du} Merle, R.~Sarkissian, and J.-Ph. Vial.
\newblock {ACCPM} -- a library for convex optimization based on an analytic
  center cutting plane method.
\newblock {Technical Report} 1995.34, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, December 1995.

\bibitem{ipm:Gondzio16}
J.~Gondzio and R.~Sarkissian.
\newblock Column generation with a primal--dual method.
\newblock {Logilab Technical Report} 96.6, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva, Switzerland, June
  1996.

\bibitem{ipm:Gondzio15}
J.~Gondzio, R.~Sarkissian, and J.-Ph. Vial.
\newblock Using an interior point method for the master problems in a
  decomposition approach.
\newblock {\em European Journal of Operational Research}, 101:577--587, 1997.

\bibitem{ipm:Gondzio19}
J.~Gondzio, R.~Sarkissian, and J.-Ph. Vial.
\newblock Parallel implementation of a central decomposition method for solving
  large scale planning problems.
\newblock {Logilab Technical Report} 98.1, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva~4, Switzerland,
  January 1998.

\bibitem{ipm:Gondzio3}
J.~Gondzio and D.~Tachat.
\newblock The design and application of the {IMPLO -- A FORTRAN} library for
  linear optimization with interior point methods.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  28:37--56, 1994.

\bibitem{ipm:Gondzio7}
J.~Gondzio and T.~Terlaky.
\newblock A computational view of interior point methods.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
  Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
  Applications}, pages 103--144. Oxford Science Publications, Oxford University
  Press, Oxford, Great Britain, 1996.

\bibitem{ipm:Gondzio18}
J.~Gondzio and J.-Ph. Vial.
\newblock Warm start and epsilon--subgradients in the cutting plane scheme for
  block--angular linear programs.
\newblock {Logilab Technical Report} 97.1, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva~4, Switzerland,
  June 1997.

\bibitem{ipm:Gong1}
D.~P. Gong and S.~R. Xu.
\newblock An interior point algorithm for solving linear programming problems
  with hybrid constraints.
\newblock {\em Sinica Naturalis Univ.\,Sunyatsemi}, 31(4):19--25, 1992.
\newblock (In Chinese, English summary).

\bibitem{ipm:Gonzaga28}
C.~C. Gonzaga.
\newblock {\em {Interior--Point Algorithms}}.
\newblock Brooks\,\&\,Cole Publishing Company, Pacific Grove, CA, USA.
\newblock (In preparation).

\bibitem{ipm:Gonzaga13}
C.~C. Gonzaga.
\newblock A conical projection algorithm for linear programming.
\newblock Memorandum UCB/ERL~M85/61, Electronics Research Laboratory,
  University of California, Berkeley, CA~94720, USA, July 1985.

\bibitem{ipm:Gonzaga1}
C.~C. Gonzaga.
\newblock New results in conical projection methods for mathematical
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
  FL, USA}, Department of Electrical Engineering and Computer Science,
  University of California, Berkeley, CA~94720, USA, October 1986.

\bibitem{ipm:Gonzaga17}
C.~C. Gonzaga.
\newblock Trust region minimization in conical projection algorithms.
\newblock {Talk held at the Eleventh IFORS International Conference on
  Operations Research in Buenos Aires, Argentina}, Department of Electrical
  Engineering and Computer Science, University of California, Berkeley,
  CA~94720, USA, August 1987.

\bibitem{ipm:Gonzaga15}
C.~C. Gonzaga.
\newblock A simple representation of {Karmarkar's} algorithm.
\newblock {Technical Report}, Department of Systems Engineering and Computer
  Science, COPPE Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro,
  RJ, Brazil, May 1988.

\bibitem{ipm:Gonzaga6}
C.~C. Gonzaga.
\newblock An algorithm for solving linear programming problems in ${O(n^{3}L)}$
  operations.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 1--28. Springer Verlag, New York,
  1989.

\bibitem{ipm:Gonzaga5}
C.~C. Gonzaga.
\newblock Conical projection algorithms for linear programming.
\newblock {\em Mathematical Programming}, 43:151--173, 1989.

\bibitem{ipm:Gonzaga20}
C.~C. Gonzaga.
\newblock Path--following algorithms for linear and quadratic programming.
\newblock {Talk held at the Third SIAM Conference on Optimization in Boston,
  MA, USA}, Department of Systems Engineering and Computer Science, COPPE
  Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil, April
  1989.

\bibitem{ipm:Gonzaga18}
C.~C. Gonzaga.
\newblock Convergence of the large step primal affine--scaling algorithm for
  primal nondegenerate linear programs.
\newblock {Technical Report} ES--230/90, Department of Systems Engineering and
  Computer Science, COPPE Federal University of Rio de Janeiro,
  21941~Rio~de~Janeiro, RJ, Brazil, September 1990.

\bibitem{ipm:Gonzaga11}
C.~C. Gonzaga.
\newblock Large steps potential reduction algorithms for linear programming.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Department of Systems Engineering and Computer Science, COPPE Federal
  University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil, July 1990.

\bibitem{ipm:Gonzaga10}
C.~C. Gonzaga.
\newblock A larger step path--following potential reduction algorithm for
  linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Department of Systems Engineering and Computer Science, COPPE
  Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil,
  January 1990.

\bibitem{ipm:Gonzaga9}
C.~C. Gonzaga.
\newblock An overview of ${O(\sqrt{n}L)}$--iteration algorithms for linear
  programming.
\newblock {Talk held at the 14th Conference on the Mathematics of Operations
  Research in Dalfsen, The Netherlands}, Department of Systems Engineering and
  Computer Science, COPPE Federal University of Rio de Janeiro,
  21941~Rio~de~Janeiro, RJ, Brazil, January 1990.

\bibitem{ipm:Gonzaga4}
C.~C. Gonzaga.
\newblock Polynomial affine algorithms for linear programming.
\newblock {\em Mathematical Programming}, 49:7--21, 1990.

\bibitem{ipm:Gonzaga3}
C.~C. Gonzaga.
\newblock Interior point algorithms for linear programming problems with
  inequality constraints.
\newblock {\em Mathematical Programming}, 52:209--225, 1991.

\bibitem{ipm:Gonzaga21}
C.~C. Gonzaga.
\newblock An interior trust region method for linearly constrained
  optimization.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:55--66, August 1991.

\bibitem{ipm:Gonzaga7}
C.~C. Gonzaga.
\newblock Large steps path--following methods for linear programming,
  {Part\,I\,: Barrier} function method.
\newblock {\em SIAM Journal on Optimization}, 1:268--279, 1991.

\bibitem{ipm:Gonzaga8}
C.~C. Gonzaga.
\newblock Large steps path--following methods for linear programming,
  {Part\,II\,: Potential} reduction method.
\newblock {\em SIAM Journal on Optimization}, 1:280--292, 1991.

\bibitem{ipm:Gonzaga14}
C.~C. Gonzaga.
\newblock On lower bound updates in primal potential reduction methods for
  linear programming.
\newblock {\em Mathematical Programming}, 52:415--428, 1991.

\bibitem{ipm:Gonzaga16}
C.~C. Gonzaga.
\newblock On the convergence of the large step affine--scaling algorithm for
  linear programming.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Systems Engineering and Computer Science,
  COPPE Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil,
  July 1991.

\bibitem{ipm:Gonzaga2}
C.~C. Gonzaga.
\newblock Search directions for interior linear programming methods.
\newblock {\em Algorithmica}, 6:153--181, 1991.

\bibitem{ipm:Gonzaga23}
C.~C. Gonzaga.
\newblock Ellipsoidal trust regions and prox functions for linearly constrained
  nonlinear programs.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Systems Engineering and Computer Science, COPPE
  Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil, May
  1992.

\bibitem{ipm:Gonzaga19}
C.~C. Gonzaga.
\newblock Path following methods for linear programming.
\newblock {\em SIAM Review}, 34(2):167--227, 1992.

\bibitem{ipm:Gonzaga30}
C.~C. Gonzaga.
\newblock On the complexity of linear programming.
\newblock {\em Resenhas do Instituto de Matem{\'a}tica e Estat{\'i}st{\'i}ca da
  Universidade de S$\tilde{a}$o Paulo}, 2:197--207, 1995.

\bibitem{ipm:Gonzaga32}
C.~C. Gonzaga.
\newblock Complexity of predictor--corrector algorithms for {LCP} based on a
  large neighborhood of the central path.
\newblock {Technical Report}, Department of Mathematics, Federal University of
  Santa Catarina, 88040--970~Florianopolis, SC, Brazil, 1996.

\bibitem{ipm:Gonzaga27}
C.~C. Gonzaga.
\newblock The largest step path following algorithm for monotone linear
  complementarity problems.
\newblock {\em Mathematical Programming}, 76:309--332, 1997.

\bibitem{ipm:Gonzaga31}
C.~C. Gonzaga and J.~F. Bonnans.
\newblock Fast convergence of the simplified largest step path following
  algorithm.
\newblock {\em Mathematical Programming}, 76:95--115, 1997.

\bibitem{ipm:Gonzaga22}
C.~C. Gonzaga and L.~A. Carlos.
\newblock A primal affine--scaling algorithm for linearly constrained convex
  programs.
\newblock {Technical Report} ES--238/90, Department of Systems Engineering and
  Computer Science, COPPE Federal University of Rio de Janeiro,
  21941~Rio~de~Janeiro, RJ, Brazil, December 1990.

\bibitem{ipm:Gonzaga29}
C.~C. Gonzaga and H.~J. Lara.
\newblock A note on properties of condition numbers.
\newblock {Technical Report}, Department of Mathematics, Federal University of
  Santa Catarina, 88040--970~Florianopolis, SC, Brazil, March 1996.

\bibitem{ipm:Gonzaga26}
C.~C. Gonzaga and R.~A. Tapia.
\newblock A quadratically convergent primal--dual algorithm for linear
  programming.
\newblock {Technical Report}, Department of Mathematical Sciences, Rice
  University, Houston, TX~77251, USA, 1993.
\newblock (In preparation).

\bibitem{ipm:Gonzaga25}
C.~C. Gonzaga and R.~A. Tapia.
\newblock On the convergence of the {Mizuno--Todd--Ye} algorithm to the
  analytic center of the solution set.
\newblock {\em SIAM Journal on Optimization}, 7:47--65, 1997.

\bibitem{ipm:Gonzaga24}
C.~C. Gonzaga and R.~A. Tapia.
\newblock On the quadratic convergence of the simplified {Mizuno--Todd--Ye}
  algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 7:66--85, 1997.

\bibitem{ipm:Gonzaga12}
C.~C. Gonzaga and M.~J. Todd.
\newblock An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine
  algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:349--359, 1992.

\bibitem{ipm:GonzalezLima2}
M.~D. Gonzalez-Lima.
\newblock Effective computation of the analytic center of the solution set in
  linear programming using primal--dual interior--point methods.
\newblock {Technical Report} TR~94--48, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1994.

\bibitem{ipm:GonzalezLima3}
M.~D. Gonz{\'a}lez-Lima, R.~A. Tapia, and F.~A. Potra.
\newblock On effectively computing the analytic center of the solution set by
  primal--dual interior--point methods.
\newblock {\em SIAM Journal on Optimization}, 8:1--25, 1998.

\bibitem{ipm:GonzalezLima1}
M.~D. Gonz{\'a}lez-Lima, R.~A. Tapia, and R.~M. Thrall.
\newblock On the construction of strong complementarity slackness solutions for
  {DEA} linear programming problems using a primal--dual interior--point
  method.
\newblock {\em Annals of Operations Research}, 66:139--162, 1996.

\bibitem{ipm:Gonzalez1}
C.~{Gonzalez Martin} and M.~{Sanchez Garcia}.
\newblock The method of {Karmarkar}\,: {A} study of its variants.
\newblock {\em Trabajos de Investigacion Operativa}, 6(1):3--25, 1991.
\newblock (In Spain, English summary).

\bibitem{ipm:Granville1}
S.~Granville.
\newblock Optimal reactive dispatch through interior point methods.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:136--146, 1994.

\bibitem{ipm:Granville2}
S.~Granville, O.~C.~O. Mello, and A.~C.~G. Mello.
\newblock Application of interior point methods to power flow unsolvability.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 11:1096--1103, 1996.

\bibitem{ipm:Gray1}
P.~Gray, J.~A. Kaliski, and Y.~Ye.
\newblock An implementation of the build--up interior method for linear
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, College of Business, Department of Management Sciences,
  University of Iowa, Iowa City, IA~52242, USA, May 1991.

\bibitem{ipm:Grayson1}
M.~A. Grayson.
\newblock The basin of attraction for interior point linear programming
  algorithms.
\newblock {Research Report} RC~15969, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1990.

\bibitem{ipm:Greenberg1}
H.~J. Greenberg.
\newblock The use of the optimal partition in a linear programming solution for
  postoptimal analysis.
\newblock {\em Operations Research Letters}, 15:179--185, 1994.

\bibitem{ipm:Greenberg4}
H.~J. Greenberg.
\newblock Rim sensitivity analysis from an interior solution.
\newblock {Technical Report} CCM--86, Center of Computational Mathematics,
  Department of Mathematics, University of Colorado at Denver, Denver,
  CO~80217, USA, October 1996.

\bibitem{ipm:Greenberg2}
H.~J. Greenberg.
\newblock Matrix sensitivity analysis from an interior solution of a linear
  program.
\newblock {Technical Report}, Center of Computational Mathematics, Department
  of Mathematics, University of Colorado at Denver, Denver, CO~80217, USA,
  1997.

\bibitem{ipm:Greenberg3}
H.~J. Greenberg, A.~G. Holder, C.~Roos, and T.~Terlaky.
\newblock On the dimension of the set of rim pertubations for optimal partition
  invariance.
\newblock {\em SIAM Journal on Optimization}, 9:207--216, 1999.

\bibitem{ipm:Grigoriadis1}
M.~D. Grigoriadis and L.~G. Khachiyan.
\newblock An interior point method for bordered block--diagonal linear
  programs.
\newblock {\em SIAM Journal on Optimization}, 6:913--932, 1996.

\bibitem{ipm:Groetschel1}
M.~Gr{\"o}tschel.
\newblock {Patente f{\"u}r mathematische Algorithmen. (Patents for mathematical
  algorithms)}.
\newblock {\em Mitteilungen der Deutschen Mathematiker--Vereinigung}, {Heft
  2}:52--56, April 1991.
\newblock (In German).

\bibitem{ipm:Grover3}
L.~K. Grover.
\newblock A force based approach to interior point algorithms for linear
  programming.
\newblock {Technical Report}, School of Electrical Engineering, Cornell
  University, Ithaca, NY~14853, USA, 1990.

\bibitem{ipm:Grover2}
L.~K. Grover.
\newblock Interior point methods for unimodular linear programming.
\newblock {Technical Report}, School of Electrical Engineering, Cornell
  University, Ithaca, NY~14853, USA, 1990.

\bibitem{ipm:Grover1}
L.~K. Grover.
\newblock Strongly polynomial interior point algorithm for a class of linear
  programming problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, School of Electrical Engineering, Cornell University, Ithaca,
  NY~14853, USA, October 1990.

\bibitem{ipm:Grover4}
L.~K. Grover.
\newblock Fast interior point methods for bipartite matching.
\newblock {\em SIAM Journal on Optimization}, 5:740--769, 1995.

\bibitem{ipm:Gu1}
M.~Gu.
\newblock On primal--dual interior point methods for semidefinite programming.
\newblock {CAM Technical Report} 97--12, Department of Mathematics, University
  of California, Los Angelos, CA, USA, March 1997.

\bibitem{ipm:Gueler5}
O.~G{\"u}ler.
\newblock An interior point algorithm for nonlinear monotone complementarity
  problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, October 1990.

\bibitem{ipm:Gueler4}
O.~G{\"u}ler.
\newblock Path following and potential reduction algorithms for nonlinear
  monotone complementarity problems.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1991.

\bibitem{ipm:Gueler8}
O.~G{\"u}ler.
\newblock Generalized linear complementarity problems and interior point
  algorithms for their solutions.
\newblock {Technical Report}, Faculty of Technical Mathematics and Computer
  Science, TU Delft, NL--2600~GA~Delft, The Netherlands, April 1992.
\newblock See also G{\"u}ler \cite{ipm:Gueler14}.

\bibitem{ipm:Gueler11}
O.~G{\"u}ler.
\newblock Complexity of smooth convex programming and its applications.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 180--202. World Scientific Publishing Co., London,
  United Kingdom, 1993.

\bibitem{ipm:Gueler2}
O.~G{\"u}ler.
\newblock Existence of interior points and interior paths in nonlinear monotone
  complementarity problems.
\newblock {\em Mathematics of Operations Research}, 18(1):128--147, 1993.

\bibitem{ipm:Gueler9}
O.~G{\"u}ler.
\newblock Limiting behavior of the weighted central paths in linear
  programming.
\newblock {\em Mathematical Programming}, 66:347--363, 1994.

\bibitem{ipm:Gueler14}
O.~G{\"u}ler.
\newblock Generalized linear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 20:441--448, 1995.
\newblock See also G{\"u}ler \cite{ipm:Gueler8}.

\bibitem{ipm:Gueler10}
O.~G{\"u}ler.
\newblock Barrier functions in interior point methods.
\newblock {\em Mathematics of Operations Research}, 21:860--885, 1996.

\bibitem{ipm:Gueler15}
O.~G{\"u}ler.
\newblock Hyperbolic polynomials and interior point methods for convex
  programming.
\newblock {\em Mathematics of Operations Research}, 22:350--377, 1997.

\bibitem{ipm:Gueler13}
O.~G{\"u}ler.
\newblock On the self--concordance of the universal barrier function.
\newblock {\em SIAM Journal on Optimization}, 7:295--303, 1997.

\bibitem{ipm:Gueler6}
O.~G{\"u}ler, {D. den} Hertog, C.~Roos, T.~Terlaky, and T.~Tsuchiya.
\newblock Degeneracy in interior point methods for linear programming.
\newblock {\em Annals of Operations Research}, 46/47:107--138, 1993.

\bibitem{ipm:Gueler7}
O.~G{\"u}ler, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock Interior point approach to the theory of linear programming.
\newblock {Cahiers de Recherche} 1992.3, Faculte des Sciences Economique et
  Sociales, Universite de Geneve, Geneve, Switzerland, 1992.
\newblock To appear in {\em Management Science}.

\bibitem{ipm:Gueler16}
O.~G{\"u}ler, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock A survey of the implications of the behavior of the central path for
  the duality theory of linear programming.
\newblock {\em Management Science}, 41:1922--1934, 1995.

\bibitem{ipm:Gueler17}
O.~G{\"u}ler and L.~Tun{\c c}el.
\newblock Invariant barrier functions on homogeneous cones.
\newblock {Research Report}, Department of Combinatorics and Optimization,
  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada,
  1997.
\newblock (In preparation).

\bibitem{ipm:Gueler12}
O.~G{\"u}ler and L.~Tun{\c c}el.
\newblock Characterization of the barrier parameter of homogeneous convex
  cones.
\newblock {\em Mathematical Programming}, 81:55--76, 1998.

\bibitem{ipm:Gueler3}
O.~G{\"u}ler and Y.~Ye.
\newblock Convergence behavior of some interior point algorithms.
\newblock {Working Paper} 91--04, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.
\newblock To appear in {\em Mathematical Programming 1993}.

\bibitem{ipm:Gueler1}
O.~G{\"u}ler and Y.~Ye.
\newblock Interior point algorithms for {LP} generate strictly complementary
  solutions.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Management Science, University of Iowa, Iowa
  City, IA~52242, USA, May 1991.

\bibitem{ipm:Guenzel1}
H.~G{\"u}nzel.
\newblock Linear programming\,: {The} central path extends analytically.
\newblock {Preprint}~67, Lehrstuhl C f{\"u}r Mathematik, RWTH Aachen,
  Templergraben 55, D--52056 Aachen, Germany, February 1996.

\bibitem{ipm:Guo4}
T.-D. Guo.
\newblock An interior point method for convex quadratic programming based on
  predictor--corrector procedure.
\newblock {\em J. Qufu Norm. Univ., Nat. Sci.}, 21:1--6, 1995.
\newblock (In Chinese).

\bibitem{ipm:Guo7}
T.-D. Guo and F.~Wu.
\newblock Interior ellipsoid method for convex quadratic programming.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
  19(?):46--50, 1996.

\bibitem{ipm:Guo8}
T.-D. Guo and F.~Wu.
\newblock An extension of predictor--corrector algorithm to a class of convex
  separable program.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
  13:362--370, 1997.

\bibitem{ipm:Guo6}
T.-D. Guo and S.~Wu.
\newblock A modified homogeneous and self--dual linear programming algorithm.
\newblock {\em Systems Science and Mathematical Sciences}, 8:270--277, 1995.

\bibitem{ipm:Guo5}
T.-D. Guo and S.~Wu.
\newblock Properties of primal interior point methods for {QP}.
\newblock {\em Optimization}, 37:227--238, 1996.

\bibitem{ipm:Guo2}
T.-D. Guo and S.-Q. Wu.
\newblock An interior point algorithm for convex programming.
\newblock {\em Qufu Shifan Daxue Xuebao Ziran Kexue Ban}, 20(Suppl.):1--7,
  1994.
\newblock (In Chinese, English summary).

\bibitem{ipm:Guo3}
T.-D. Guo and S.-Q. Wu.
\newblock Interior point methods for convex quadratic programming.
\newblock {\em Qufu Shifan Daxue Xuebao Ziran Kexue Ban}, 20:51--62, 1994.
\newblock (In Chinese, English summary).

\bibitem{ipm:Guo1}
T.-D. Guo and S.-Q. Wu.
\newblock Predictor--corrector algorithm for convex quadratic programming with
  upper bounds.
\newblock {\em Journal of Computational Mathematics}, 13:161--171, 1995.

\bibitem{ipm:Gupta1}
A.~Gupta.
\newblock Graph partitioning based sparse matrix orderings for interior--point
  algorithms.
\newblock {Technical Report} RC\,20467\,(90480), IBM Research Division,
  T.\,J.\,Watson Research Center, Yorktown Heights, New York, NY~10598, May
  1996.

\bibitem{ipm:Gupta3}
S.~Gupta and N.~S. Chaudhari.
\newblock Study and implementation of a primal--dual
  infeasible--interior--point algorithm.
\newblock {\em Proceedings of the Mathematical Society}, 12:41--46, 1996.

\bibitem{ipm:Gupta2}
S.~Gupta and N.~S. Chaudhari.
\newblock A primal--dual formulation of general linear programming problem for
  {Karmarkar's} approach.
\newblock {\em Journal of the Indian Academical Mathematics}, 19:223--230,
  1997.

\bibitem{ipm:Haeberly2}
J.-P.~A. Haeberly, M.~Nayakkankuppam, and M.~L. Overton.
\newblock Extending {Mehrotra and Gondzio} higher order methods to mixed
  semidefinite--quadratic--linear programming.
\newblock {\em Optimization Methods and Software}, 1998/99.

\bibitem{ipm:Haeberly1}
J.-P.~A. Haeberly and M.~L. Overton.
\newblock Optimizing eigenvalues of symmetric definite pencils.
\newblock {\em Proceedings of the 1994 American Control Conference (Baltimore,
  MD, USA, June/July 1994)}, 1:836--839, 1994.

\bibitem{ipm:Hafsteinsson1}
H.~Hafsteinsson, R.~Levkovitz, and G.~Mitra.
\newblock Solving large scale linear programming problems using an interior
  point method on a massively parallel {SIMD} computer.
\newblock volume~4 of {\em Applied Parallel Computing}, pages 301--316. Gordon
  and Breach Publishers, London, United Kingdom, 1993.

\bibitem{ipm:Haglin1}
D.~Haglin, J.~Kaliski, C.~Roos, and T.~Terlaky.
\newblock Logarithmic barrier decomposition methods for semi--definite
  programming.
\newblock {Technical Report} 96--51, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2628~CD~Delft, The Netherlands, 1996.

\bibitem{ipm:Hajian1}
M.~Hajian, R.~Levkovitz, and G.~Mitra.
\newblock A branch and bound algorithm for discrete programming using the
  interior point method and the simplex method.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 257--265. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Halicka2}
M.~Halick{\'a}.
\newblock Analytic properties of the central path at boundary point in linear
  programming.
\newblock {\em Mathematical Programming}, 84:335--355, 1999.

\bibitem{ipm:Halicka1}
M.~Halick{\'a} and M.~Hamala.
\newblock Duality of transformation functions in the interior point methods.
\newblock {\em Acta Mathematica Universitatis Comenianae (Comenius University
  Czechoslovakia)}, 65:229--245, 1996.

\bibitem{ipm:Hall1}
L.~A. Hall and R.~J. Vanderbei.
\newblock Two--third is sharp for affine scaling.
\newblock {\em Operations Research Letters}, 13:197--201, 1993.

\bibitem{ipm:Hamala1}
M.~Hamala.
\newblock A general approach to interior point transformation methods for
  mathematical programming.
\newblock {\em Acta Mathematica Universitatis Comenianae (Comenius University
  Czechoslovakia)}, 54/55:243--266, 1989.

\bibitem{ipm:Hamilton1}
B.~C. Hamilton and D.~E. Stein.
\newblock {AT~\&~T's KORBX System\,: Solving} the unsolvable.
\newblock {\em AT~\&~T Technology}, 4(3):36--41, 1989.

\bibitem{ipm:Haemmerlin1}
G.~H{\"a}mmerlin and K.~H. Hoffmann.
\newblock {\em Numerische Mathematik}, chapter 9.4.4\,: {Polynomiale
  Algorithmen}, pages 424--430.
\newblock Springer Verlag, Berlin, Germany, second edition, 1991.
\newblock (In German).

\bibitem{ipm:Han2}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock Computational aspect of an interior point algorithm for quadratic
  programming problems with box constraints.
\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
  Optimization, Papers from the Workshop held at Cornell University, Ithaca,
  NY, USA, October 1989}, volume~46 of {\em SIAM Proceedings in Applied
  Mathematics}, pages 92--112. Society of Industrial and Applied Mathematics
  (SIAM), Philadelphia, PA, USA, 1990.

\bibitem{ipm:Han6}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock Interior point algorithms for quadratic programming problems.
\newblock {\em Proceedings of the Conference on Optimization Methods and Their
  Applications (Nauka, USSR)}, pages 194--213, 1990.
\newblock (In Russian).

\bibitem{ipm:Han1}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock Interior point approaches to nonconvex programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Computer Science Department, The Pennsylvania State University,
  University Park, PA~16802, USA, October 1990.

\bibitem{ipm:Han3}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock On potential reduction algorithms for some entropy optimization
  problems.
\newblock {Technical Report} CS--91--02, Computer Science Department, The
  Pennsylvania State University, University Park, PA~16802, USA, 1991.

\bibitem{ipm:Han4}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock Solving some engineering problems using an interior--point algorithm.
\newblock {Technical Report} CS--91--04, Computer Science Department, The
  Pennsylvania State University, University Park, PA~16802, USA, 1991.

\bibitem{ipm:Han7}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock Implementation of interior--point algorithms for some entropy
  optimization problems.
\newblock {\em Optimization Methods and Software}, 1:71--80, 1992.

\bibitem{ipm:Han5}
C.~G. Han, P.~M. Pardalos, and Y.~Ye.
\newblock On the solution of indefinite quadratic problems using an interior
  point algorithm.
\newblock {\em Informatica}, 3:474--496, 1992.

\bibitem{ipm:Handschin1}
E.~Handschin, M.~Langer, and E.~Kliokys.
\newblock Interior point method for state estimation with current magnitude
  measurements and inequality constraints.
\newblock {\em Proceedings of the 1995 IEEE Power Industry Computer Application
  Conference (Salt Lake City, UT, USA, 1995)}, pages 385--391, 1995.
\newblock See also Kliokys et al. \cite{ipm:Kliokys1}.

\bibitem{ipm:Hane1}
C.~A. Hane, C.~Barnhart, E.~L. Johnson, R.~E. Marsten, G.~L. Nemhauser, and
  G.~Sigismondi.
\newblock The fleet assignment problem\,: {Solving} a large--scale integer
  program.
\newblock {\em Mathematical Programming}, 70:211--232, 1995.

\bibitem{ipm:Harker1}
P.~T. Harker and B.~Xiao.
\newblock A polynomial--time algorithm for affine variational inequalities.
\newblock {\em Applied Mathematics Letters}, 4(2):31--34, 1991.

\bibitem{ipm:Haverly1}
C.~A. Haverly.
\newblock Behavior of the simplex and {Karmarkar} algorithms.
\newblock {Talk held at the 12th Symposium on Mathematical Programming in
  Cambridge, MA, USA}, Haverly Systems Inc., Denville, NJ~07834, USA, 1985.

\bibitem{ipm:Haverly3}
C.~A. Haverly.
\newblock Results of a new series of case runs using {Karmarkar's} algorithm.
\newblock {Technical Report}, Haverly Systems Inc., Denville, NJ~07834, USA,
  1985.

\bibitem{ipm:Haverly2}
C.~A. Haverly.
\newblock Studies on behavior of the {Karmarkar} method.
\newblock {Technical Report}, Haverly Systems Inc., Denville, NJ~07834, USA,
  1985.

\bibitem{ipm:He1}
B.~He, {E. de} Klerk, C.~Roos, and T.~Terlay.
\newblock Method of approximate centers for semi--definite programming.
\newblock {\em Optimization Methods and Software}, 7:291--309, 1997.

\bibitem{ipm:Heindl1}
G.~Heindl.
\newblock {Eine Implementierung des Karmarkar Verfahrens~(An implementation of
  Karmarkar's algorithm)}.
\newblock {Interner Bericht der intergrierten Arbeitsgruppe Mathematische
  Probleme aus dem Ingenieurbereich}, Fachbereich Mathematik, Gesamthochschule
  Wuppertal, D--42097~Wuppertal~1, Germany, February 1985.
\newblock (In German).

\bibitem{ipm:Heinkenschloss1}
M.~Heinkenschloss and L.~N. Vicente.
\newblock Analysis of inexact trust--region interior--point {SQP} algorithms.
\newblock {Technical Report} TR~95--18, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1995.

\bibitem{ipm:Helmberg1}
C.~Helmberg.
\newblock {\em An interior point method for semi--definite programming and
  max--cut bounds}.
\newblock PhD thesis, Department of Mathematics, Graz University of Technology,
  A--8010 Graz, Austria, October 1994.

\bibitem{ipm:Helmberg3}
C.~Helmberg.
\newblock Fixing variables in semidefinite relaxations.
\newblock {Preprint} SC--96--43, Konrad--Zuse Zentrum f{\"u}r
  Informationstechnik Berlin, D--14195~Berlin--Dahlem, Germany, December 1996.

\bibitem{ipm:Helmberg5}
C.~Helmberg, S.~Poljak, F.~Rendl, and H.~Wolkowicz.
\newblock Combining semidefinite and polyhedral relaxations for integer
  programs.
\newblock In E.~Balas and J.~Clausen, editors, {\em Integer Programming and
  Combinatorial Optimization (Proceedings of the 4th International IPCO
  Conference, Copenhagen, Denmark, May 1995)}, volume 920 of {\em Lecture Notes
  in Computer Science}, pages 124--134. Springer Verlag, Berlin, Germany, 1995.

\bibitem{ipm:Helmberg4}
C.~Helmberg and F.~Rendl.
\newblock A spectral bundle method for semidefinite programming.
\newblock {ZIB Preprint} SC--97--37, Konrad--Zuse Zentrum f{\"u}r
  Informationstechnik Berlin, D--14195~Berlin--Dahlem, Germany, August 1997.

\bibitem{ipm:Helmberg2}
C.~Helmberg, F.~Rendl, R.~J. Vanderbei, and H.~Wolkowicz.
\newblock An interior--point method for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 6:342--361, 1996.

\bibitem{ipm:Helmke1}
U.~Helmke.
\newblock Isospectral flows and linear programming.
\newblock {\em Journal of the Australian Mathematical Society, Series\,B},
  34:495--510, 1993.

\bibitem{ipm:Hemmer1}
G.~M. Hemmer.
\newblock Computational issues in the interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Mathematics, Northwestern Illinois University, Chicago,
  IL~60625, USA, April 1992.

\bibitem{ipm:Hernandez1}
S.~Hernandez, J.~Mata, and J.~Doria.
\newblock Optimization of large structural systems by using {Karmarkar's}
  method.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, University of Zaragoza, Zaragoza, Spain, May 1992.

\bibitem{ipm:Herskovits1}
J.~Herskovits and J.~Asquier.
\newblock A quasi--{N}ewton interior point algorithm for nonlinear constrained
  optimization.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Center of
  Technology, COPPE Federal University of Rio de Janeiro, 21941 Rio de Janeiro,
  Brazil, August 1990.

\bibitem{ipm:Herskovits2}
J.~Herskovits, E.~Laporte, P.~{Le~Tallec}, and G.~Santos.
\newblock A quasi--{Newton} interior point algorithm applied to constrained
  optimum design in computational fluid dynamics.
\newblock {\em Revue Europ{\'e}enne des {\'E}l{\'e}ments Finis}, 5:595--617,
  1996.

\bibitem{ipm:Hertog1}
{D. den} Hertog.
\newblock Interior point methods for linear programming.
\newblock Master's thesis, Faculty of Mathematics and Informatics, TU Delft,
  NL--2628~BL~Delft, The Netherlands, May 1989.

\bibitem{ipm:Hertog16}
{D. den} Hertog.
\newblock {\em {Interior Point Approach to Linear, Quadratic and Convex
  Programming, Algorithms and Complexity}}, volume 277 of {\em Mathematics and
  Its Applications}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Hertog17}
{D. den} Hertog, F.~Jarre, C.~Roos, and T.~Terlaky.
\newblock A unifying investigation of interior--point methods for convex
  programming.
\newblock {Technical Report} 92--89, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1992.

\bibitem{ipm:Hertog20}
{D. den} Hertog, F.~Jarre, C.~Roos, and T.~Terlaky.
\newblock A sufficient condition for self--concordance, with application to
  some classes of structured convex programming problems.
\newblock {\em Mathematical Programming}, 69:75--88, 1995.

\bibitem{ipm:Hertog19}
{D. den} Hertog, J.~A. Kaliski, C.~Roos, and T.~Terlaky.
\newblock A logarithmic barrier cutting plane method for convex programming.
\newblock {\em Annals of Operations Research}, 58:69--98, 1995.

\bibitem{ipm:Hertog18}
{D. den} Hertog, J.~A. Kaliski, C.~Roos, and T.~Terlaky.
\newblock A note on central cutting plane methods for convex programming.
\newblock {\em Annals of Operations Research}, 58:69--98, 1995.

\bibitem{ipm:Hertog2}
{D. den} Hertog and C.~Roos.
\newblock A survey of search directions in interior point methods for linear
  programming.
\newblock {\em Mathematical Programming}, 52:481--509, 1991.

\bibitem{ipm:Hertog3}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A potential reduction method for a class of smooth convex programming
  problems.
\newblock {Technical Report} 90--01, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1990.
\newblock Rewritten in den Hertog et al.\ \cite{ipm:Hertog12}.

\bibitem{ipm:Hertog15}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock Iri's polynomiality proof for the {Iri--Imai} method recast.
\newblock {Technical Report} 91--74, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1991.

\bibitem{ipm:Hertog8}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A polynomial method of weighted centers for convex quadratic
  programming.
\newblock {\em Journal of Information \& Optimization Sciences},
  12(2):187--205, 1991.

\bibitem{ipm:Hertog6}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A potential reduction variant of {R}enegar's short--step
  path--following method for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:43--68, 1991.

\bibitem{ipm:Hertog9}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A build--up variant of the path--following method for {LP}.
\newblock {\em Operations Research Letters}, 12:181--186, 1992.

\bibitem{ipm:Hertog12}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A large--step analytic center method for a class of smooth convex
  programming problems.
\newblock {\em SIAM Journal on Optimization}, 2:55--70, 1992.

\bibitem{ipm:Hertog4}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock On the classical logarithmic barrier function method for a class of
  smooth convex programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 73:1--25,
  1992.

\bibitem{ipm:Hertog14}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock On the monotonicity of the dual objective along barrier paths.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Bulletin}, 20:2--7, 1992.

\bibitem{ipm:Hertog13}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock Adding and deleting constraints in a path--following method for
  linear programming.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 166--185. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Hertog7}
{D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock Inverse barrier methods for linear programming.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  28:123--133, 1994.

\bibitem{ipm:Hertog5}
{D. den} Hertog, C.~Roos, and J.-Ph. Vial.
\newblock An ${O(n^{0.5}L)}$ complexity reduction for long step path following
  methods for linear programming.
\newblock Revised version of {Technical Report} 89--85, Faculty of Mathematics
  and Informatics, TU Delft, NL--2628~BL~Delft, The Netherlands, 1990.
\newblock Rewritten in den Hertog et al.\ \cite{ipm:Hertog10}.

\bibitem{ipm:Hertog11}
{D. den} Hertog, C.~Roos, and J.-Ph. Vial.
\newblock Polynomial--time long--steps algorithms for linear programming based
  on the use of the logarithmic barrier function.
\newblock {Unpublished Manuscript}, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1990.
\newblock Talk given by C. Roos at the Conference on Progress in Mathematical
  Programming in Asilomar, CA, USA, February 1990.

\bibitem{ipm:Hertog10}
{D. den} Hertog, C.~Roos, and J.-Ph. Vial.
\newblock A complexity reduction for the long--step path--following algorithm
  for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:71--87, 1992.

\bibitem{ipm:Herzel1}
S.~Herzel, M.~C. Recchioni, and F.~Zirilli.
\newblock A quadratically convergent method for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:255--289, 1991.

\bibitem{ipm:Herzel2}
S.~Herzel and M.~J. Todd.
\newblock Two interior--point algorithms for a class of convex programming
  problems.
\newblock {\em Optimization Methods and Software}, 5:27--55, 1995.

\bibitem{ipm:Hettich1}
R.~Hettich and G.~Margraff.
\newblock Some experiments with {Karmarkar's} algorithm.
\newblock {\em Optimization}, 19:653--664, 1988.

\bibitem{ipm:Hettich2}
R.~Hettich and M.~Ries.
\newblock A modified scaling algorithm for {LP}.
\newblock {\em Optimization}, 21:709--721, 1990.

\bibitem{ipm:Hillier1}
F.~S. Hillier and G.~J. Lieberman.
\newblock {\em Introduction to Operations Research}, chapter 4.9\,: {N}ew
  developments, pages 100--104, chapter\,9.4\,: {A}n interior--point algorithm,
  pages 312--323.
\newblock McGraw--Hill, fifth edition, 1990.

\bibitem{ipm:Hipolito2}
A.~Hipolito.
\newblock A long step linear programming algorithm based on quasi--{Newton}
  inverse barrier centering.
\newblock {Research Report} 91--12, Department of Industrial and Systems
  Engineering, University of Florida, Gainesville, FL~32611, USA, October 1991.

\bibitem{ipm:Hipolito1}
A.~Hipolito.
\newblock A long step inverse barrier hybrid algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Industrial and Systems Engineering, University of
  Florida, Gainesville, FL~32611, USA, April 1992.
\newblock See Hipolito \cite{ipm:Hipolito2}.

\bibitem{ipm:Hipolito4}
A.~Hipolito and D.~W. Hearn.
\newblock An interior point based bundle method for decomposition and nonsmooth
  optimization.
\newblock {Manuscript}, Department of Industrial and Systems Engineering,
  University of Florida, Gainesville, FL~32611, USA, 1995.
\newblock (In preparation).

\bibitem{ipm:Hipolito3}
A.~L. Hipolito.
\newblock A weighted least squares study of robustness in interior point linear
  programming.
\newblock {\em Computational Optimization and Applications}, 2:29--46, 1993.

\bibitem{ipm:Ho1}
J.~K. Ho.
\newblock Linear programming with spreadsheet macros.
\newblock {Technical Report}, Management Science Program, University of
  Tennessee, 615--SMC, Knoxville, TN~37996--0562, USA, 1987.

\bibitem{ipm:Hoffmann1}
A.~J. Hoffmann, M.~Mannos, D.~Sokolowsky, and N.~Wiegmann.
\newblock Computational experience in solving linear programs.
\newblock {\em Journal of the Society for Industrial and Applied Mathematics
  (SIAM)}, 1:17--33, 1953.

\bibitem{ipm:Honig1}
R.~Honig and G.~I. Balistreri.
\newblock Implementation of the {Karmarkar} algorithm on a transputer network.
\newblock Master's thesis, Faculty of Electrical Engineering, Delft University
  of Technology, NL--2628~BL~Delft, The Netherlands, October 1989.

\bibitem{ipm:Hooker1}
J.~N. Hooker.
\newblock Karmarkar's linear programming algorithm.
\newblock {\em Interfaces}, 16(4):75--90, 1986.
\newblock Errata in {\em Interfaces}, 17(1):128, 1987.

\bibitem{ipm:Hotta2}
K.~Hotta, M.~Inaba, and A.~Yoshise.
\newblock A complexity analysis of a smoothing method using
  {Chen--Harker--Kanzow--S--functions} for monotone linear complementarity
  problems.
\newblock {Discussion Paper Series} 807, Institute of Policy and Planning
  Sciences, University of Tsukuba, Tsukuba, Ibaraki 305, Japan, 1999.

\bibitem{ipm:Hotta1}
K.~Hotta and A.~Yoshise.
\newblock Global convergence of a class of non--interior--point algorithms
  using {Chen--Harker--Kanzow} functions for nonlinear complementary problems.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
  1004:40--70, 1997.

\bibitem{ipm:Houck1}
D.~Houck.
\newblock Introduction to the {AT~\&~T~KORBX System}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA, October 1988.

\bibitem{ipm:Hough1}
P.~D. Hough and S.~A. Vavasis.
\newblock Complete orthogonal decomposition for weighted least squares.
\newblock {Preprint}, School of Operations Research and Industrial Engineering,
  Cornell University, Ithaca, NY~14853, USA, March 1995.

\bibitem{ipm:Housos1}
E.~C. Housos, C.~C. Huang, and J.~M. Liu.
\newblock Parallel vector computational considerations on the {AT~\&~T~KORBX
  System}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, AT~\&~T~Bell Laboratories, Holmdel, NJ~07733, USA, October 1988.

\bibitem{ipm:Housos2}
E.~C. Housos, C.~C. Huang, and J.~M. Liu.
\newblock Parallel algorithms for the {AT~\&~T~KORBX System}.
\newblock {\em AT~\&~T~Technical Journal}, 68:37--47, 1989.

\bibitem{ipm:Hsieh1}
Y.-C. Hsieh and D.~L. Brucker.
\newblock New infeasible interior--point algorithm based on monomial method.
\newblock {\em Computers and Operations Research}, 23:653--666, 1996.

\bibitem{ipm:Hu1}
T.~C. Hu.
\newblock Linear programming algorithms and computational results, 1987.
\newblock Panel--Discussion at the ORSA/TIMS Joint National Meeting in
  St.~Louis, October 1987.

\bibitem{ipm:Huang9}
C.~Huang, B.~Yu, and Y.~Wang.
\newblock A new interior path following method for nonconvex nonlinear
  programming.
\newblock {\em Northeastern Mathematical Journal}, 13:257--260, 1997.

\bibitem{ipm:Huang1}
S.~Huang.
\newblock A primal--dual algorithm for linear programming.
\newblock {Technical Report}, College of Business Administration, University of
  Iowa, Iowa City, IA~52240, USA, 1989.

\bibitem{ipm:Huang5}
S.~Huang, J.~Ji, and F.~Potra.
\newblock A superlinearity convergent {$O(\sqrt{n} L)$}--iteration
  predictor--corrector algorithm for linear complementarity problems.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, College of Business Administration, University of Iowa, Iowa City,
  IA~52240, USA, May 1992.

\bibitem{ipm:Huang2}
S.~Huang and K.~O. Kortanek.
\newblock A simultaneous primal-- and dual--potential reduction algorithm for
  linear programming.
\newblock {Working Paper Series} 89--2, College of Business Administration,
  University of Iowa, Iowa City, IA~52240, USA, 1989.

\bibitem{ipm:Huang3}
S.~Huang and K.~O. Kortanek.
\newblock A large--step simultaneous primal--dual potential reduction algorithm
  for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, College of Business Administration, University of Iowa, Iowa City,
  IA~52240, USA, October 1990.

\bibitem{ipm:Huang4}
S.~Huang and K.~O. Kortanek.
\newblock A note on a potential reduction algorithm for {LP} with simultaneous
  primal--dual updating.
\newblock {\em Operations Research Letters}, 10:501--507, 1991.

\bibitem{ipm:Huang7}
S.~Huang and K.~O. Kortanek.
\newblock On the length of primal--dual projection of potential reduction
  algorithm.
\newblock {\em Optimization}, 34:161--171, 1995.

\bibitem{ipm:Huang8}
S.~Huang and K.~O. Kortanek.
\newblock A hybrid polynomial algorithm for linear programming.
\newblock {\em Systems Science and Mathematical Sciences}, 9:67--75, 1996.

\bibitem{ipm:Huang6}
S.~Huang and Y.~Ye.
\newblock On the average number of iterations of the polynomial interior--point
  algorithms for linear programming.
\newblock {Working Paper Series} 91--16, Department of Management Sciences,
  University of Iowa, Iowa City, IA~52240, USA, 1991.

\bibitem{ipm:Huard1}
P.~Huard.
\newblock Resolution of mathematical programming with nonlinear constraints by
  the method of centers.
\newblock In J.~Abadie, editor, {\em Nonlinear Programming}, pages 207--219.
  North Holland, Amsterdam, The Netherlands, 1967.

\bibitem{ipm:Huard2}
P.~Huard.
\newblock A method of centers by upper--bounding functions with applications.
\newblock In J.~B. Rosen, O.~L. Mangasarian, and K.~Ritter, editors, {\em
  Nonlinear Programming\,: Proceedings of a Symposium held at the University of
  Wisconsin, Madison, Wisconsin, USA, May 1970}, pages 1--30. Academic Press,
  New York, USA, 1970.

\bibitem{ipm:Huard3}
P.~Huard and B.~T. Lieu.
\newblock La methode des centres dans un espace topologique.
\newblock {\em Numerische Mathematik}, 8:56--67, 1968.
\newblock (In French).

\bibitem{ipm:Huhn1}
P.~Huhn.
\newblock {\em {Schranken f{\"u}r die durchschnittliche Laufzeit des
  Simplexverfahrens und von Innere--Punkte--Verfahren (Bounds for the average
  running time of the simplex--method and od interior--point methods)}}.
\newblock PhD thesis, Mathematische Naturwissentschaftliche Fakult{\"a}t,
  Universit{\"a} Augsburg, Augsburg, Germany, August 1997.
\newblock In German, English Summary. Published as\,: {\it{Augsburger
  Mathematisch--Naturwissentschaftliche Schriften 16, 223pp., Dr.\, Bernd
  Wi{\ss}ner Verlag, Augsburg, Germany, ISBN\,3--89639--067--8, 1997}}.

\bibitem{ipm:Hung1}
P.~F. Hung and Y.~Ye.
\newblock An asymptotically {$O(\sqrt{n}L)$} iteration algorithm that uses long
  steps.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, March 1994.
\newblock See also Hung and Ye \cite{ipm:Hung2}.

\bibitem{ipm:Hung2}
P.~F. Hung and Y.~Ye.
\newblock An asymptotical $o(\sqrt{n}l)$--iteration path--following linear
  programming algorithm that uses wide neighborhoods.
\newblock {\em SIAM Journal on Optimization}, 6:570--586, 1996.

\bibitem{ipm:Hurd1}
J.~K. Hurd and F.~H. Murphy.
\newblock Exploiting special structure in primal dual interior point methods.
\newblock {\em ORSA Journal on Computing}, 4:38--44, 1992.

\bibitem{ipm:Hwang1}
T.-M. Hwang, C.-H. Lin, W.-W. Lin, and S.-C. Fang.
\newblock A relaxed primal--dual path following algorithm for linear
  programming.
\newblock {\em Annals of Operations Research}, 62:173--196, 1996.

\bibitem{ipm:IBM1}
{\emph{Optimization Subroutine Library (OSL)\,: Guide and References}}.
\newblock Manual, IBM Corporation, Kingston, USA, 1991.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Ignizio1}
J.~P. Ignizio and T.~M. Cavalier.
\newblock {\em {Linear Programming}}, chapter 7\,: {Alternatives} to the
  simplex algorithm, pages 247--271.
\newblock Prentice Hall, Englewood Cliffs, NJ~07632, USA, 1994.

\bibitem{ipm:Ikura1}
Y.~Ikura and D.~Stein.
\newblock Computational experience with a {Karmarkar--based} approach to solve
  multi--period, multi--refinery production models.
\newblock {Talk held at the 12th Triennial Conference on Operations Research in
  Athens, Greece}, AT~\&~T~Bell Laboratories, June 1990.

\bibitem{ipm:Illes2}
T.~Ill{\'e}s, J.~Peng, C.~Roos, and T.~Terlaky.
\newblock A strongly polynomial rounding procedure yielding a maximally
  complementary solution for {$P_*(\kappa)$} linear complementarity problems.
\newblock {Technical Report} 98--15, Faculty of Information Technology and
  Systems Subfaculty of Technical Mathematics and Informatics, Department of
  Statistics, Stochastic and Operations Research, Delft University of
  Technology,, P.O. Box 5031, 2600 GA Delft, The Netherlands, July 1998.

\bibitem{ipm:Illes1}
T.~Ill{\'e}s, C.~Roos, and T.~Terlaky.
\newblock Polynomial affine--scaling algorithms for ${P_{*}(\kappa)}$ linear
  complementarity problems.
\newblock In P.~Gritzmann, R.~Horst, E.~Sachs, and R.~Tichatschke, editors,
  {\em {Recent Advances in Optimization (Trier, Germany, 1996)}}, volume 452 of
  {\em Lecture Notes in Economics and Mathematical Systems}, pages 119--137.
  Springer Verlag, Berlin, Germany, 1997.

\bibitem{ipm:Imae1}
J.~Imae, T.~Furudate, and S.~Sugawara.
\newblock A simple numerical method for minimizing the maximum eigenvalues of
  symmetric matrices via nonlinear differential equation solvers.
\newblock {\em Proceedings of the 35th IEEE conference on Decision and
  Control}, 4/4:4514--4525, 1996.

\bibitem{ipm:Imai1}
H.~Imai.
\newblock Extensions of the multiplicative penalty function for linear
  programming.
\newblock {\em Journal of the Operations Research Society of Japan},
  30:160--179, 1987.

\bibitem{ipm:Imai2}
H.~Imai.
\newblock On the convexity of the multiplicative version of {Karmarkar's}
  potential function.
\newblock {\em Mathematical Programming}, 40:29--32, 1988.

\bibitem{ipm:Imai3}
H.~Imai.
\newblock Recent trends in linear programming.
\newblock {\em Journal of the Institute of Electronics, Information and
  Communication Engineers (Japan)}, 72(10):1053--1058, 1989.
\newblock (In Japanese).

\bibitem{ipm:Imai4}
H.~Imai.
\newblock On the polynomiality of the multiplicative penalty function method
  for linear programming and related inscribed ellipsoids.
\newblock {\em Transactions of the Institute of Electronics, Information and
  Communication Engineers (Japan)}, E74(4):669--671, April 1991.

\bibitem{ipm:Iri1}
M.~Iri.
\newblock Another 'simple and fast' algorithm for linear programming.
\newblock {Talk held at the 12th Symposium on Mathematical Programming in
  Cambridge, MA, USA}, Department of Mathematical Engineering and
  Instrumentation Physics, University of Tokyo, Tokyo, Japan, 1985.

\bibitem{ipm:Iri2}
M.~Iri.
\newblock Integrability of vector and polyvector fields associated with
  interior point methods.
\newblock {\em Mathematical Programming}, 52:511--525, 1991.

\bibitem{ipm:Iri6}
M.~Iri.
\newblock A proof of the polynomiality of the {Iri--Imai} method for linear
  programming.
\newblock {\em Journal of Complexity}, 9:269--290, 1993.

\bibitem{ipm:Iri3}
M.~Iri and H.~Imai.
\newblock A multiplicative penalty function for linear programming-- another
  ''new and fast'' algorithm.
\newblock {\em Proceedings of the 6th Mathematical Programming Symposium of
  Japan, Tokyo, Japan}, pages 97--120, 1985.

\bibitem{ipm:Iri4}
M.~Iri and H.~Imai.
\newblock A multiplicative barrier function method for linear programming.
\newblock {\em Algorithmica}, 1(4):455--482, 1986.

\bibitem{ipm:Iri5}
M.~Iri and H.~Imai.
\newblock Theory of the multiplicative penalty function method for linear
  programming.
\newblock In D.~S. Johnson, T.~Nishizeki, A.~Nozaki, and H.~S. Wilf, editors,
  {\em Discrete Algorithms and Complexity\,: Proceedings of the Japan--US Joint
  Seminar, Kyoto, Japan, June 1986}, pages 417--435. Academic Press, New York,
  1987.

\bibitem{ipm:Irisarri2}
G.~D. Irisarri, L.~M. Kimball, K.~A. Clements, A.~Bagchi, and P.~W. Davis.
\newblock Economic dispatch with network and ramping constraints via interior
  point methods.
\newblock {\em IEEE Transactions on Power Systems}, 13:236--242, 1998.

\bibitem{ipm:Irisarri1}
G.~D. Irisarri, X.~Wang, J.~Tong, and S.~Mokhtari.
\newblock Maximum loadability of power systems using interior point nonlinear
  optimization method.
\newblock {\em IEEE Transactions on Power Systems}, 12:162--172, 1997.

\bibitem{ipm:Ishihara1}
T.~Ishihara and M.~Kojima.
\newblock On the {\em big m} in the affine scaling algorithm.
\newblock {\em Mathematical Programming}, 62:85--93, 1993.

\bibitem{ipm:Ito3}
S.~Ito.
\newblock An interior point method for linear programming problems on a
  function space.
\newblock {\em Proceedings of the Institute Statistical Mathematics},
  42:239--246, 1994.
\newblock (In Japanese).

\bibitem{ipm:Ito2}
S.~Ito.
\newblock A primal--dual interior--point algorithm for state--constrained {LQ}
  optimal control problems.
\newblock {\em Proceedings of the 1995 American Control Conference (Seattle,
  WA, USA, June 1995)}, 3:2077--2078, 1995.

\bibitem{ipm:Ito1}
S.~Ito, C.~T. Kelley, and E.~W. Sachs.
\newblock Inexact primal--dual interior point iteration for linear programs in
  function spaces.
\newblock {\em Computational Optimization and Applications}, 4:189--201, 1995.

\bibitem{ipm:Iusem4}
A.~Iusem and R.~D.~C. Monteiro.
\newblock On dual convergence of the generalized proximal point method with
  {Bregman} distances.
\newblock {Manuscript}, School of Industrial and Systems Engineering, Georgia
  Institute of Technology, Atlanta, GA~30322, USA, October 1997.

\bibitem{ipm:Iusem1}
A.~N. Iusem.
\newblock An interior point multiplicative method for optimization under
  positivity constraints.
\newblock {\em Acta Applicatae Mathematicae}, 38:163--184, 1995.

\bibitem{ipm:Iusem3}
A.~N. Iusem.
\newblock An interior point method for the nonlinear complementarity problem.
\newblock {\em Applied Numerical Mathematics}, 24:469--482, 1997.

\bibitem{ipm:Iusem2}
A.~N. Iusem, B.~F. Svaiter, and M.~Teboulle.
\newblock Multiplicative interior gradient methods for minimization over the
  nonnegative orthant.
\newblock {\em SIAM Journal on Control and Optimization}, 34:389--406, 1996.

\bibitem{ipm:Izhutkin1}
V.~S. Izhutkin, M.~V. Petropavlovski{\v{o}}, and A.~V. Blinov.
\newblock The center and the barrier function methods using reduced directions
  for the nonlinear programming problem.
\newblock {\em Izvestiya Vyssihikh Uchebnykh Zavedemi{\v{i}} Matematika}, pages
  30--41, 1996.
\newblock (In Russian. Translated in {\emph{Russian Mathematics}}).

\bibitem{ipm:Jamsek1}
J.~Jam{\u{s}}ek.
\newblock Karmarkar's algorithm for linear programming.
\newblock {\em Obzornik za Matematiko in Fiziko}, 38(6):161--169, 1991.
\newblock (In Slovenian, English summary).

\bibitem{ipm:Jan3}
G.~M. Jan.
\newblock {\em A new variant of the primal affine scaling algorithm for linear
  programs}.
\newblock PhD thesis, Department of Operations Research, North Carolina State
  University, Raleigh, NC~27695-7913, USA, July 1990.

\bibitem{ipm:Jan1}
G.~M. Jan and S.-C. Fang.
\newblock A variant of affine--scaling method for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, North Carolina State University, Raleigh, NC~27695-7913, USA, October
  1989.
\newblock See Jan \cite{ipm:Jan3}, and Jan and Fang \cite{ipm:Jan2}.

\bibitem{ipm:Jan2}
G.~M. Jan and S.-C. Fang.
\newblock A new variant of the primal affine scaling method for linear
  programs.
\newblock {\em Optimization}, 22(5):681--715, 1991.

\bibitem{ipm:Janacek1}
J.~Janacek.
\newblock {Perspektivy Karmarkarova algorithmu v linearnim programovani
  (Perspectives of Karmarkar's algorithm in linear programming)}.
\newblock {\em Ekonomicko--Matematicky Obzor (Czechoslovakia)}, 25(1):50--63,
  1989.
\newblock (In Czech).

\bibitem{ipm:Jansen6}
B.~Jansen.
\newblock An introduction to interior point algorithms for linear and convex
  quadratic programming.
\newblock {Technical Report} 9276/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, The Netherlands, 1992.

\bibitem{ipm:Jansen19}
B.~Jansen.
\newblock {\em {Interior Point Techniques in Optimization\,: Complexity,
  Sensitivity and Algorithms}}, volume~6 of {\em Applied Optimization}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.

\bibitem{ipm:Jansen12}
B.~Jansen, {J. J. de} Jong, C.~Roos, and T.~Terlaky.
\newblock Sensitivity analysis in linear programming\,: {Just} be careful\,!
\newblock {\em European Journal of Operational Research}, 101:15--28, 1997.

\bibitem{ipm:Jansen1}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock An interior point approach to postoptimal and parametric analysis in
  linear programming.
\newblock {Technical Report} 92--21, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2628~CD~Delft, The Netherlands, April 1992.
\newblock New subtitle: {\em Optimal bases versus optimal partitions for
  postoptimal analysis in linear programming}.

\bibitem{ipm:Jansen5}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock On {Vaidya's} volumetric center method for convex programming.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 289--295. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Jansen3}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Primal--dual algorithms for linear programming based on the
  logarithmic barrier method.
\newblock {\em Journal of Optimization Theory and Applications}, 83:1--26,
  1994.

\bibitem{ipm:Jansen4}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock The theory of linear programming\,: {Skew} symmetric self--dual
  problems and the central path.
\newblock {\em Optimization}, 29:225--233, 1994.

\bibitem{ipm:Jansen14}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A new algorithm for the computation of the smallest eigenvalue of a
  symmetric matrix and its eigenspace.
\newblock {Technical Report} 95--70, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Jansen13}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A short survey on ten years interior point methods.
\newblock {Technical Report} 95--45, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Jansen16}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Interior point methods, a decade after {Karmarkar} -- {A} survey,
  with application to the smallest eigenvalue problem.
\newblock {\em Statistica Nederlandica}, 50:146--170, 1996.

\bibitem{ipm:Jansen17}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Introduction to the theory of interior point methods.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 3--34. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Jansen10}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Long--step primal--dual target--following algorithms for linear
  programming.
\newblock {\em Mathematical Models of Operations Research}, 44:11--30, 1996.

\bibitem{ipm:Jansen7}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A polynomial primal--dual {Dikin}--type algorithm for linear
  programming.
\newblock {\em Mathematics of Operations Research}, 21:341--353, 1996.

\bibitem{ipm:Jansen18}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Target--following methods for linear programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 83--124. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Jansen9}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A family of polynomial affine scaling algorithms for positive
  semidefinite linear complementarity problems.
\newblock {\em SIAM Journal on Optimization}, 7:126--140, 1997.

\bibitem{ipm:Jansen2}
B.~Jansen, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock Interior--point methodology for linear programming\,:\, {Duality},
  sensitivity analysis and computational aspects.
\newblock In K.~Frauendorfer, H.~Glavitsch, and R.~Bacher, editors, {\em
  Optimization in Planning and Operation of Electric Power Systems (Lecture
  Notes of the SVOR/ASRO Tutorial, Thun, Switzerland, October 14--16, 1992)},
  pages 57--123. Physica Verlag (A Springer Company), Heidelberg, Germany,
  1993.
\newblock See also Roos \cite{ipm:Roos21}.

\bibitem{ipm:Jansen8}
B.~Jansen, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock Primal--dual target--following algorithms for linear programming.
\newblock {\em Annals of Operations Research}, 62:197--231, 1996.

\bibitem{ipm:Jansen11}
B.~Jansen, C.~Roos, T.~Terlaky, and Y.~Ye.
\newblock Improved complexity using higher--order correctors for primal--dual
  {Dikin} affine scaling.
\newblock {\em Mathematical Programming}, 76:117--130, 1997.

\bibitem{ipm:Jansen15}
B.~Jansen, C.~Roos, T.~Terlaky, and A.~Yoshise.
\newblock Polynomiality of primal--dual affine scaling algorithms for nonlinear
  complementarity problems.
\newblock {\em Mathematical Programming}, 78:315--345, 1997.

\bibitem{ipm:Jarre14}
F.~Jarre.
\newblock On the convergence of the method of analytic centers when applied to
  convex quadratic programs.
\newblock {DFG--Report}~35, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, 1987.
\newblock Preliminary version of Jarre \cite{ipm:Jarre1}.

\bibitem{ipm:Jarre6}
F.~Jarre.
\newblock Convergence of the method of analytic centers for generalized convex
  programs.
\newblock DFG--Report~67, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany, May
  1988.
\newblock Revised October 1988. The revised version is identical to Jarre
  \cite{ipm:Jarre3}.

\bibitem{ipm:Jarre2}
F.~Jarre.
\newblock The method of analytic centers for smooth convex programs.
\newblock Preprint 165, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  February 1989.
\newblock See also Jarre \cite{ipm:Jarre7}.

\bibitem{ipm:Jarre7}
F.~Jarre.
\newblock {\em The method of analytic centers for smooth convex programs}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  1989.

\bibitem{ipm:Jarre3}
F.~Jarre.
\newblock On the method of analytic centers for solving smooth convex programs.
\newblock In S.~Dolecki, editor, {\em Optimization\,: Proceedings of the 5th
  French--German Conference in Castel--Novel, Varetz, France, October 1988},
  volume 1405 of {\em Lecture Notes in Mathematics}, pages 69--86. Springer
  Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Jarre4}
F.~Jarre.
\newblock A homotopy method for convex programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  January 1990.

\bibitem{ipm:Jarre8}
F.~Jarre.
\newblock Interior--point methods for convex programming.
\newblock {Technical Report} SOL~90--16, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, 1990.
\newblock See also Jarre \cite{ipm:Jarre15}.

\bibitem{ipm:Jarre1}
F.~Jarre.
\newblock On the convergence of the method of analytic centers when applied to
  convex quadratic programs.
\newblock {\em Mathematical Programming}, 49:341--358, 1990/91.

\bibitem{ipm:Jarre17}
F.~Jarre.
\newblock An efficient line--search for logarithmic barrier functions.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 296--303. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.
\newblock See also Jarre \cite{ipm:Jarre13}.

\bibitem{ipm:Jarre13}
F.~Jarre.
\newblock An efficient line search for logarithmic barrier functions.
\newblock {Technical Report} 188, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, May 1992.
\newblock For an extended abstract see Jarre \cite{ipm:Jarre17}.

\bibitem{ipm:Jarre15}
F.~Jarre.
\newblock Interior--point methods for convex programming.
\newblock {\em Applied Mathematics \& Optimization}, 26:287--311, 1992.
\newblock See also Jarre \cite{ipm:Jarre8}.

\bibitem{ipm:Jarre11}
F.~Jarre.
\newblock An interior--point method for minimizing the largest eigenvalue of a
  linear combination of matrices.
\newblock {\em SIAM Journal on Control and Optimization}, 31:1360--1377, 1993.
\newblock See also {\em NATO ASI Series E Vol.\,232 (1993), pp. 395}.

\bibitem{ipm:Jarre22}
F.~Jarre.
\newblock Interior--point methods via self--concordance or relative {Lipschitz}
  condition.
\newblock {Habilitationthesis}, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, March 1994.
\newblock See also Jarre \cite{ipm:Jarre21}.

\bibitem{ipm:Jarre19}
F.~Jarre.
\newblock A new line--search step based on the {Weierstrass}
  ${\cal{p}}$--function for minimizing a class of logarithmic barrier
  functions.
\newblock {\em Numerische Mathematik}, 68:81--94, 1994.

\bibitem{ipm:Jarre16}
F.~Jarre.
\newblock Optimal ellipsoidal approximations around the analytic center.
\newblock {\em Applied Mathematics \& Optimization}, 30:15--19, 1994.

\bibitem{ipm:Jarre21}
F.~Jarre.
\newblock Interior--point methods via self--concordance or relative {Lipschitz}
  condition.
\newblock {\em Optimization Methods and Software}, 5:75--104, 1995.
\newblock See also Jarre \cite{ipm:Jarre22}.

\bibitem{ipm:Jarre23}
F.~Jarre.
\newblock Interior--point methods for classes of convex programs.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 255--296. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Jarre26}
F.~Jarre.
\newblock A {QQP}--minimization method for semidefinite and smooth nonconvex
  programs.
\newblock {Technical Report}, Mathematisches Institut der Universit{\"a}t
  Trier, Trier, Germany, August 1998.

\bibitem{ipm:Jarre24}
F.~Jarre, M.~Kocvara, and J.~Zowe.
\newblock Interior point methods for mechanical design problems.
\newblock {Preprint} 173, Institut f{\"u}r Angewandte Mathematik,
  Universit{\"a}t Erlangen--N{\"u}rnberg, Martensstr. 3, D--91058 Erlangen,
  Germany, 1996.

\bibitem{ipm:Jarre27}
F.~Jarre, M.~Kocvara, and J.~Zowe.
\newblock Optimal truss design by interior--point methods.
\newblock {\em SIAM Journal on Optimization}, 8:1084--1107, 1998.

\bibitem{ipm:Jarre18}
F.~Jarre and S.~Mizuno.
\newblock An infeasible--interior--point algorithm using projections onto a
  convex set.
\newblock {Technical Report} 206, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, August 1993.
\newblock See also Mizuno and Jarre \cite{ipm:Mizuno23}.

\bibitem{ipm:Jarre10}
F.~Jarre and M.~A. Saunders.
\newblock An adaptive primal--dual method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:7--16, August 1991.

\bibitem{ipm:Jarre12}
F.~Jarre and M.~A. Saunders.
\newblock A practical interior--point method for convex programming.
\newblock {\em SIAM Journal on Optimization}, 5:149--171, 1995.

\bibitem{ipm:Jarre5}
F.~Jarre, G.~Sonnevend, and J.~Stoer.
\newblock An implementation of the method of analytic centers.
\newblock In A.~Bensoussan and J.~L. Lions, editors, {\em Analysis and
  Optimization of Systems}, volume 111 of {\em Lecture Notes in Control and
  Information Sciences}, pages 297--308. Springer Verlag, Berlin, Germany,
  1988.

\bibitem{ipm:Jarre9}
F.~Jarre, G.~Sonnevend, and J.~Stoer.
\newblock On the complexity of a numerical algorithm for solving generalized
  convex quadratic programs by following a central path.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 233--242. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Jarre25}
F.~Jarre and M.~Wechs.
\newblock Extending {Mehrotra's} corrector for linear programs.
\newblock {Preprint} 219, Mathematische Institute der Universit{\"a}t
  W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany, December 1996.
\newblock (Revised October 1997).

\bibitem{ipm:Jarre20}
F.~Jarre and S.~J. Wright.
\newblock On the role of the objective function in barrier methods.
\newblock {Preprint} MSC--P485--1294, Mathematics and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, December 1994.

\bibitem{ipm:Jensen3}
D.~L. Jensen and R.~Polyak.
\newblock Decomposition in {LP} based on modified barrier function.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Mathematical Sciences Department, IBM~T.~J.~Watson Research Center,
  Yorktown Heights, NY~10598, USA, May 1992.

\bibitem{ipm:Jensen2}
D.~L. Jensen, R.~Polyak, and R.~R. Schneur.
\newblock Numerical experience with the modified barrier functions method for
  linear--constrained optimization problems.
\newblock {Technical Report}, Mathematical Sciences Department,
  IBM~T.~J.~Watson Research Center, Yorktown Heights, NY~10598, USA, May 1992.
\newblock See also Polyak \cite{ipm:Polyak3}.

\bibitem{ipm:Jensen4}
D.~L. Jensen and R.~A. Polyak.
\newblock The convergence of a modified barrier method for convex programming.
\newblock {\em IBM Journal of Research and Development}, 38:307--321, 1994.

\bibitem{ipm:Jensen1}
D.~L. Jensen and A.~E. Steger.
\newblock A variation of {Karmarkar's} algorithm to solve linear programs in
  standard form.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
  CA, USA}, State University of New York, Stony Brook, NY~11794, USA, April
  1986.
\newblock See Steger \cite{ipm:Steger1}.

\bibitem{ipm:Ji5}
J.~Ji and F.~Potra.
\newblock On the average complexity of finding an {$\varepsilon$}--optimal
  solution for linear programming.
\newblock {Reports on Computational Mathematics}~25, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, March 1992.

\bibitem{ipm:Ji2}
J.~Ji and F.~Potra.
\newblock An interior--point algorithm for quadratically constrained entropy
  minimization problems.
\newblock {\em Journal of Optimization Theory and Applications}, 77:79--95,
  1993.

\bibitem{ipm:Ji8}
J.~Ji and F.~Potra.
\newblock Tapia indicators and finite termination of
  infeasible--interior--point methods for degenerate {LCP}.
\newblock In J.~Renegar, M.~Shub, and S.~Smale, editors, {\em The Mathematics
  of Numerical Analysis (1995 AMS--SIAM Summer Seminar in Applied Mathematics
  July/August 1995 held at Park City, UT, USA)}, volume~32 of {\em Lectures in
  Applied Mathematics}, pages 443--454. American Mathematical Society,
  Providence, RI~02940--6248, USA, 1996.

\bibitem{ipm:Ji4}
J.~Ji, F.~Potra, and S.~Huang.
\newblock A predictor--corrector method for linear complementarity problems
  with polynomial complexity and superlinear convergence.
\newblock {\em Journal of Optimization Theory and Applications}, 85:187--199,
  1995.

\bibitem{ipm:Ji9}
J.~Ji, F.~Potra, and R.~Sheng.
\newblock On the local convergence of a predictor--corrector method for
  semidefinite programming.
\newblock {Reports on Computational Mathematics}~98, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, 1997.

\bibitem{ipm:Ji1}
J.~Ji, F.~Potra, R.~A. Tapia, and Y.~Zhang.
\newblock An interior--point method with polynomial complexity and superlinear
  convergence for linear complementarity problems.
\newblock {Technical Report} TR--91--23, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Ji7}
J.~Ji, F.~A. Potra, and R.~Sheng.
\newblock A predictor--corrector method for solving the
  {$P_{*}(\kappa)$}--matrix {LCP} from infeasible starting points.
\newblock {\em Optimization Methods and Software}, 6:109--126, 1995.

\bibitem{ipm:Ji3}
J.~Ji and Y.~Ye.
\newblock Complexity analysis of {Karmarkar's} algorithm.
\newblock {Working Paper} 90--5, Department of Mathematics, The University of
  Iowa, Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ji6}
J.~Ji and Y.~Ye.
\newblock A complexity analysis for interior--point algorithms based on
  {Karmarkar's} potential function.
\newblock {\em SIAM Journal on Optimization}, 4:512--520, 1994.

\bibitem{ipm:Jiang1}
J.~Jiang.
\newblock A long step primal--dual path--following method for semidefinite
  programming.
\newblock {Science Report} 96009, Department of Applied Mathematics, Tsinghue
  University, Beijing~100084, China, March 1996.
\newblock To appear in {\em{Operations Research Letters}}.

\bibitem{ipm:Jiang2}
J.~Jiang and M.~Shi.
\newblock A logarithmic barrier {Newton} method for semidefinite programming.
\newblock {\em Systems Science and Mathematical Sciences}, 10(2):168--175,
  1997.

\bibitem{ipm:Jie1}
S.~Jie and J.~Zhu.
\newblock Predictor--corrector method for extended linear--quadratic
  programming.
\newblock {\em Computers and Operations Research}, 23:755--767, 1996.

\bibitem{ipm:Jing1}
X.~Jing and J.-Q. Xue.
\newblock A dual interior point algorithm for convex programming.
\newblock {\em Journal of the Northeastern University Nature Sciences},
  19:98--100, 1998.

\bibitem{ipm:Johnson1}
C.~R. Johnson, B.~Kroschel, and H.~Wolkowicz.
\newblock An interior--point method for approximate positive semidefinite
  completions.
\newblock {\em Computational Optimization and Applications}, 9:175--190, 1998.

\bibitem{ipm:Jong1}
J.~J. Jong.
\newblock A computational study of recent approaches to sensitivity analysis in
  linear programming\,: {Optimal} basis, optimal partition and optimal function
  value approach.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2600~GA~Delft, The Netherlands, 1996.

\bibitem{ipm:Joshi1}
A.~Joshi, A.~Goldstein, and P.~M. Vaidya.
\newblock A fast implementation of a path--following algorithm for maximizing a
  linear function over a network polytope.
\newblock In D.~S. Johnson and C.~C. McGeogh, editors, {\em Network Flows and
  Matching\,: First DIMACS Implementation Challenge}, volume~12 of {\em DIMACS
  Series on Discrete Mathenatics and Theoretical Computer Science}, pages
  267--298. American Mathematical Society, Providence, Rhode Island~02940, USA,
  1993.

\bibitem{ipm:Judice1}
J.~J. J{\'u}dice.
\newblock Algorithms for linear complementarity problems.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
  Optimization\,: The State--of--the--Art (Il Ciocco, Barga, Italy, September
  1993)}, volume 434 of {\em NATO Advanced Science Institute Series C\,:
  Mathematical and Physical Sciences}, pages 435--474. Kluwer Academic
  Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Jung1}
H.~W. Jung, R.~E. Marsten, and M.~J. Saltzman.
\newblock The column {C}holesky method for numerical factorization in interior
  point algorithms.
\newblock {Technical Report} 596, Department of Mathematical Sciences,Clemson
  University, Clemson, SC~29634--1907, USA, 1991.
\newblock This is subsumed by Jung et al.\ \cite{ipm:Jung2}.

\bibitem{ipm:Jung2}
H.~W. Jung, R.~E. Marsten, and M.~J. Saltzman.
\newblock Numerical factorization methods for interior point algorithms.
\newblock {\em ORSA Journal on Computing}, 6:94--105, 1994.

\bibitem{ipm:Jung3}
H.~W. Jung and M.~J. Saltzman.
\newblock The multifrontal method for numerical factorization in interior point
  algorithms.
\newblock {Technical Report} 597, Department of Mathematical Sciences, Clemson
  University, Clemson, SC~29634--1907, USA, 1991.
\newblock This is subsumed by Jung et al.\ \cite{ipm:Jung2}.

\bibitem{ipm:Kalantari4}
B.~Kalantari.
\newblock Solving linear programming by bisection and a projective feasibility
  algorithm.
\newblock {Technical Report} LCSR--TR--91, Laboratory for Computer Science
  Research, Rutgers University, New Brunswick, NJ~08903, USA, 1987.

\bibitem{ipm:Kalantari2}
B.~Kalantari.
\newblock Derivation of a generalized and strenghtened {Gordan Theorem} from
  generalized {Karmarkar} potential and logarithmic barrier functions.
\newblock {Technical Report} LCSR--TR--121, Laboratory for Computer Science
  Research, Rutgers University, New Brunswick, NJ~08903, USA, 1989.

\bibitem{ipm:Kalantari3}
B.~Kalantari.
\newblock Canonical problems for quadratic programming and projective methods
  for their solution.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 243--263. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Kalantari1}
B.~Kalantari.
\newblock Karmarkar's algorithm with improved steps.
\newblock {\em Mathematical Programming}, 46:73--78, 1990.

\bibitem{ipm:Kalantari5}
B.~Kalantari.
\newblock Generalization of {Karmarkar's} algorithm to convex homogeneous
  functions.
\newblock {\em Operations Research Letters}, 11:93--98, 1992.

\bibitem{ipm:Kalantari6}
B.~Kalantari.
\newblock A theorem of the alternative for multihomogeneous functions and its
  relationship to diagonal scaling of matrices.
\newblock {\em Linear Algebra and Its Applications}, 236:1--24, 1996.

\bibitem{ipm:Kalantari7}
B.~Kalantari and M.~R. Emamy-K.
\newblock On linear programming and matrix scaling over the algebraic numbers.
\newblock {\em Linear Algebra and Its Applications}, 262:282--305, 1997.

\bibitem{ipm:Kaliski4}
J.~A. Kaliski.
\newblock {\em A decomposition variant for large scale linear programming}.
\newblock PhD thesis, Department of Management Science, College of Business
  Administration, University of Iowa, Iowa City, IA~52240, USA, May 1992.

\bibitem{ipm:Kaliski6}
J.~A. Kaliski, D.~Haglin, C.~Roos, and T.~Terlaky.
\newblock Logarithmic barrier decomposition methods for semi--infinite
  programming.
\newblock {Technical Report} 96--51, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1996.
\newblock To appear in {\em International Transactions in Operations Reseach}.

\bibitem{ipm:Kaliski2}
J.~A. Kaliski and Y.~Ye.
\newblock Convergence behavior of {Karmarkar's} projective algorithm for
  solving a simple linear program.
\newblock {\em Operations Research Letters}, 10:389--393, 1991.

\bibitem{ipm:Kaliski1}
J.~A. Kaliski and Y.~Ye.
\newblock A decomposition variant of the potential reduction algorithm for
  linear programming.
\newblock {Working Paper} 91--11, Department of Management Science, College of
  Business Administration, University of Iowa, Iowa City, IA~52240, USA, 1991.
\newblock See also Kaliski and Ye\,\cite{ipm:Kaliski5}.

\bibitem{ipm:Kaliski3}
J.~A. Kaliski and Y.~Ye.
\newblock An extension of the potential reduction algorithm for solving the
  linear complentary problem with priority goals.
\newblock {\em Linear Algebra and Its Applications}, 193:35--50, 1993.

\bibitem{ipm:Kaliski5}
J.~A. Kaliski and Y.~Ye.
\newblock A short--cut potential reduction algorithm for linear programming.
\newblock {\em Management Science}, 39:757--776, 1993.
\newblock See also Kaliski and Ye\,\cite{ipm:Kaliski1}.

\bibitem{ipm:Kallio1}
M.~Kallio.
\newblock On gradient projection for linear programming.
\newblock Manuscript, School of Organization and Management, Yale University,
  New Haven, CT~06520, USA, 1986.

\bibitem{ipm:Kallio2}
M.~Kallio and E.~L. Porteus.
\newblock A class of methods for linear programming.
\newblock {\em Mathematical Programming}, 14:161--176, 1978.

\bibitem{ipm:Kamath11}
A.~P. Kamath.
\newblock {\em Efficient continuous algorithms for combinatorial optimization}.
\newblock PhD thesis, Department of Computer Science, Stanford University, Palo
  Alto, CA, USA, September 1995.

\bibitem{ipm:Kamath2}
A.~P. Kamath and N.~K. Karmarkar.
\newblock Continuous approach to compute upper bounds in quadratic maximization
  problems with integer constraints.
\newblock In C.~A. Floudas and P.~M. Pardalos, editors, {\em Recent Advances in
  Global Optimization}, Princeton Series in Computer Science, pages 125--140.
  Princeton University Press, Princeton, NJ, USA, 1992.

\bibitem{ipm:Kamath3}
A.~P. Kamath and N.~K. Karmarkar.
\newblock A continuous method for computing bounds in integer quadratic
  optimization problems.
\newblock {\em Journal of Global Optimization}, 2(3):229--241, 1992.

\bibitem{ipm:Kamath8}
A.~P. Kamath and N.~K. Karmarkar.
\newblock An {$O(nL)$} iteration algorithm for computing bounds in quadratic
  optimization problems.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 254--268. World Scientific Publishing Co., London,
  United Kingdom, 1993.

\bibitem{ipm:Kamath9}
A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock An approximate dual projective algorithm for solving assignment
  problems.
\newblock In D.~S. Johnson and C.~C. McGeogh, editors, {\em Network Flows and
  Matching\,: First DIMACS Implementation Challenge}, volume~12 of {\em DIMACS
  Series on Discrete Mathenatics and Theoretical Computer Science}, pages
  431--451. American Mathematical Society, Providence, Rhode Island~02940, USA,
  1993.

\bibitem{ipm:Kamath6}
A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock Computational and complexity results for an interior point algorithm
  for multicommodity flows.
\newblock {Technical Report} TR--21/93, Dipartimento di Informatica, Universita
  di Pisa, Pisa, Italy, 1993.
\newblock To appear in {\em Netflow}. See also Kamath et al.
  \cite{ipm:Kamath10}.

\bibitem{ipm:Kamath10}
A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock Computational and complexity results for an interior point algorithm
  on multi--commodity flow problems.
\newblock {Technical Report}, Department of Computer Science, Stanford
  University, Palo Alto, CA, USA, 1993.

\bibitem{ipm:Kamath1}
A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock Computational experience with an interior point algorithm on the
  satisfiability problem.
\newblock {\em Annals of Operations Research}, 25:43--58, 1990.

\bibitem{ipm:Kamath4}
A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock A continuous approach to inductive inference.
\newblock {\em Mathematical Programming}, 57:215--238, 1992.

\bibitem{ipm:Kamath5}
A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior point approach to {Boolean} vector function synthesis.
\newblock {\em Proceedings of the 36th MSCAS}, pages 185--189, 1993.

\bibitem{ipm:Kamath7}
A.~P. Kamath and O.~Palmon.
\newblock Improved interior point algorithms for exact and approximate solution
  of multicommodity flow problems.
\newblock {\em Proceedings of the Sixth Annual ACM--SIAM Symposium on Discrete
  Algorithms (San Francisco, CA, USA, January 22--24, 1995)}, pages 502--511,
  1995.

\bibitem{ipm:Kannan1}
R.~Kannan and W.~R. Pulleyblank.
\newblock {\em Integer Programming and Combinatorial Optimization}.
\newblock University of Waterloo Press, Waterloo, Ontario, Canada, 1990.

\bibitem{ipm:Kanzow1}
C.~Kanzow.
\newblock Some tools allowing interior--point methods to become noninterior.
\newblock {Preprint (Hamburger Beitr{\"a}ge zur Angewandten Mathematik)}
  79--1994, Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t Hamburg,
  Hamburg, Germany, 1994.

\bibitem{ipm:Kaplan1}
A.~Kaplan and R.~Tichatschke.
\newblock Proximal methods in view of interior point strategies.
\newblock {\em Journal of Optimization Theory and Applications}, 98:399--429,
  1998.

\bibitem{ipm:Kapoor1}
S.~Kapoor and P.~M. Vaidya.
\newblock Fast algorithms for convex quadratic programming and multicommodity
  flows.
\newblock {\em Proceedings of the 18th Annual ACM Symposium on Theory of
  Computing}, pages 147--159, 1986.

\bibitem{ipm:Kapoor2}
S.~Kapoor and P.~M. Vaidya.
\newblock An extension of {Karmarkar's} interior point method to convex
  quadratic programming.
\newblock {Technical Report}, Department of Computer Science, University of
  Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1988.

\bibitem{ipm:Kapoor3}
S.~Kapoor and P.~M. Vaidya.
\newblock Speeding--up {Karmarkar's} algorithm for multicommodity flows.
\newblock {\em Mathematical Programming}, 73:111--127, 1996.
\newblock A preliminary version is given in Kapoor and Vaidya
  \cite{ipm:Kapoor1}.

\bibitem{ipm:Karisch1}
S.~E. Karisch and F.~Rendl.
\newblock Semidefinite programming and graph equipartion.
\newblock {Technical Report} 302--CDLDO~55, Department of Mathematics, Graz
  University of Technology, Graz, Austria, December 1995.

\bibitem{ipm:Karisch2}
S.~E. Karisch, F.~Rendl, and J.~Clausen.
\newblock Solving graph bisection problems with semidefinite programming.
\newblock {Technical Report} DIKU--TR--97/9, Department of Computer Science,
  University of Copenhagen, Copenhagen, Denmark, July 1997.

\bibitem{ipm:Karisch3}
S.~E. Karisch, F.~Rendl, H.~Wolkowicz, and Q.~Zhao.
\newblock Semidefinite programming relaxations for the quadratic assignment
  problem.
\newblock {Technical Report} CORR\,95--27, Department of Combinatorics and
  Optimization, Fasculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, September 1996.

\bibitem{ipm:Karloff1}
H.~Karloff.
\newblock {\em Linear Programming}, chapter 5\,: {Karmarkar's} algorithm, pages
  103--130.
\newblock Birkh{\"a}user Verlag, Basel, Switzerland, 1991.

\bibitem{ipm:Karmarkar1}
N.~K. Karmarkar.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {\em Proceedings of the 16th Annual ACM Symposium on Theory of
  Computing}, pages 302--311, 1984.

\bibitem{ipm:Karmarkar2}
N.~K. Karmarkar.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {\em Combinatorica}, 4:373--395, 1984.

\bibitem{ipm:Karmarkar3}
N.~K. Karmarkar.
\newblock Some comments on the significance of the new polynomial--time
  algorithm for linear programming.
\newblock {Technical Report}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974,
  USA, 1984.

\bibitem{ipm:Karmarkar18}
N.~K. Karmarkar.
\newblock Why is the new algorithm better than simplex method and ellipsoid
  method~?
\newblock {Extended Abstract}, AT~\&~T~Bell Laboratories, Murray Hill,
  NJ~07974, USA, 1984/85.

\bibitem{ipm:Karmarkar16}
N.~K. Karmarkar.
\newblock Recent developments in new approaches to linear programming.
\newblock {Talk held at the SIAM Conference on Optimization, Houston, TX, USA},
  AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, 1987.

\bibitem{ipm:Karmarkar4}
N.~K. Karmarkar.
\newblock An interior--point approach to {NP}--complete problems.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, July 1988.

\bibitem{ipm:Karmarkar5}
N.~K. Karmarkar.
\newblock Methods and apparatus for efficient resource allocation.
\newblock U.S.~Patent No.~4.744.028, 1988.
\newblock AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA.

\bibitem{ipm:Karmarkar19}
N.~K. Karmarkar.
\newblock An interior--point approach to {NP}--complete problems -- {Part I}.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 297--308. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Karmarkar6}
N.~K. Karmarkar.
\newblock Riemannian geometry underlying interior--point methods for linear
  programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 51--75. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Karmarkar22}
N.~K. Karmarkar.
\newblock A new parallel architecture for sparse matrix computation based on
  finite projective geometries.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Proceedings of
  Supercomputing\,'91}, pages 358--369. IEEE Computer Society, New York, USA,
  1991.

\bibitem{ipm:Karmarkar15}
N.~K. Karmarkar.
\newblock Interior--point methods in optimization.
\newblock In {\em Proceedings of the Second International Conference on
  Industrial and Applied Mathematics (ICIAM~'91), Washington, DC, July, 1991},
  pages 160--181. SIAM Publications, Philadelphia, PA, USA, 1992.

\bibitem{ipm:Karmarkar14}
N.~K. Karmarkar, J.~C. Lagarias, L.~Slutsman, and P.~Wang.
\newblock Power--series variants of {Karmarkar--type} algorithms.
\newblock {\em AT~\&~T Technical Journal}, 68:20--36, 1989.

\bibitem{ipm:Karmarkar7}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Further developments in the new polynomial--time algorithm for linear
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Boston, MA,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA, May 1985.

\bibitem{ipm:Karmarkar8}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Implementation and computational aspects of the {Karmarkar} algorithm
  for linear programming, using an iterative method for computing projections.
\newblock {Technical Memorandum}, AT~\&~T Bell Laboratories, Murray Hill,
  NJ~07974, USA, 1989.
\newblock See Karmarkar and Ramakrishnan \cite{ipm:Karmarkar9}.

\bibitem{ipm:Karmarkar10}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Robust control system models and their solution by the {Karmarkar}
  algorithm.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, AT~\&~T
  Bell Laboratories, Murray Hill, NJ~07974, USA, July 1990.

\bibitem{ipm:Karmarkar9}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Computational results of an interior point algorithm for large scale
  linear programming.
\newblock {\em Mathematical Programming}, 52:555--586, 1991.

\bibitem{ipm:Karmarkar12}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior point algorithm for zero--one integer programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ 07974, USA, October 1988.

\bibitem{ipm:Karmarkar20}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior--point approach to the maximum independent set problem in
  dense random graphs.
\newblock {Manuscript}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA,
  1988/1990.

\bibitem{ipm:Karmarkar13}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock Further developments on an interior point algorithm for zero--one
  integer programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, January
  1990.

\bibitem{ipm:Karmarkar17}
N.~K. Karmarkar, M.~G.~C. Resende, and K.~G. Ramakrishnan.
\newblock An interior point algorithm to solve computationally difficult set
  covering problems.
\newblock {\em Mathematical Programming}, 52:597--618, 1991.

\bibitem{ipm:Karmarkar11}
N.~K. Karmarkar and L.~P. Sinha.
\newblock Application of {Karmarkar's} algorithm to overseas telecommunications
  facilities planning.
\newblock {Talk held at the 12th International Symposium on Mathematical
  Programming in Boston, MA, USA}, AT~\&~T Bell Laboratories, Murray Hill,
  NJ~07974, USA, August 1985.

\bibitem{ipm:Karmarkar21}
N.~K. Karmarkar and S.~Thakur.
\newblock An interior--point approach to tensor optimization with application
  to upper bounds in integer quadratic optimization problems.
\newblock {\em Proceedings of Second Integer programming and Combinatorial
  Optimization Conference (Carnegie--Mellon University, Pittsburgh, PA, 1992)},
  pages 406--420, 1992.

\bibitem{ipm:Karypis2}
G.~Karypis, A.~Gupta, and V.~Kumar.
\newblock A parallel formulation of interior point algorithms.
\newblock In {\em Proceedings Supercomputing\,'94 (Washington, D.C., USA,
  November 1994)}, pages 204--213. IEEE Computer Society, New York, NY, USA,
  1994.

\bibitem{ipm:Karypis1}
G.~Karypis, A.~Gupta, and V.~Kumar.
\newblock A highly parallel interior point algorithm.
\newblock {\em Proceedings of the 7th SIAM Conference on Parallel Processing
  for Scientific Computing}, pages 110--112, 1995.

\bibitem{ipm:Kas1}
P.~Kas, E.~Klafszky, L.~Malyusz, and G.~Izbirak.
\newblock Minimization of {Bregman's} divergence functions, and its relation to
  linear programming.
\newblock {Technical Report}, Department of Building Management and
  Organization, Technical University of Budapest, Muegyetem rkp.\,3, Budapest,
  1111~Hungary, 1998.

\bibitem{ipm:Kaeschel1}
J.~K{\"a}schel.
\newblock Karmarkar--{\"a}hnliche {Verfahren in der Linearen Optimierung
  (Karmarkar--type procedures in linear programming)}.
\newblock {Talk held at the DGOR--Jahrestagung in Stuttgart--Hohenheim,
  Germany}, Sektion Wirtschaftswissenschaften, TU Chemnitz, P.~O.~Box~964,
  D--9010~Chemnitz, East--Germany, September 1991.

\bibitem{ipm:Kaeschel2}
J.~K{\"a}schel.
\newblock {'' An efficient algorithm for linear programming '' of V. Ch.
  Venkaiah}.
\newblock {\em Proceedings of the Indian Academy of Sciences, Mathematical
  Sciences}, 102(2):155--158, 1992.
\newblock See also Venkaiah\,\cite{ipm:Venkaiah1}.

\bibitem{ipm:Katsura1}
R.~Katsura, M.~Fukushima, and T.~Ibaraki.
\newblock Interior methods for nonlinear minimum cost network flow problems.
\newblock {\em Journal of the Operations Research Society of Japan},
  32:174--179, 1989.

\bibitem{ipm:Kelly1}
T.~K. Kelly and J.~G. Ecker.
\newblock {EPM\,: An} exterior point method for linear programming.
\newblock {Technical Report}, April 1997.

\bibitem{ipm:Kennings1}
A.~A. Kennings, V.~H. Quintana, and A.~Vannelli.
\newblock Constraint matrix ordering for interior point algorithms on hypercube
  multiprocessors.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
  Symposium (Manhattan, KS, USA, September 1994)}, 1:187--195, 1994.

\bibitem{ipm:Kennings2}
A.~A. Kennings and A.~Vannelli.
\newblock An efficient interior point approach for {QP} and {LP} models of the
  relative placement problem.
\newblock {\em Proceedings of the 39th Midwest Symposium on Circuits and
  Systems}, 1/3:443--446, 1996.

\bibitem{ipm:Kennington1}
J.~L. Kennington.
\newblock Using {KORBX} for military airlift applications.
\newblock {\em Proceedings of the 28th IEEE Conference on Decision and
  Control}, pages 1603--1605, December 1989.

\bibitem{ipm:Keraghel1}
A.~Keraghel.
\newblock {\em Etude adaptive et comparative des prinicipales variantes dans
  l'algorithme de {Karmarkar}}.
\newblock PhD thesis, Laboratoire ARTEMIS (IMAG), Universite Joseph Fourier,
  BP~68, F--38402 St.~Martin d'Heres Cedex, France, 1989.
\newblock (In French).

\bibitem{ipm:Khachian1}
L.~G. Khachian and M.~J. Todd.
\newblock On the complexity of approximating the maximal inscribed ellipsoid
  for a polytope.
\newblock {Technical Report} 893, School of Operations Research and Industrial
  Engineering, College of Engineering, Cornell University, Ithaca,
  NY~14853--3801, USA, 1990.

\bibitem{ipm:Kim3}
K.~Kim.
\newblock {\em The effective integration of simplex and interior point
  techniques. {Part\,I\,: Decomposition, Part\,II\,: Null--space affine
  scaling}}.
\newblock PhD thesis, Department of Pure and Applied Mathematics, Washington
  State University, Pullman, WA~99164--3113, USA, 1991.
\newblock According to Part\,I see Kim and Nazareth \cite{ipm:Kim1}, for
  Part\,II see Kim and Nazareth \cite{ipm:Kim4}.

\bibitem{ipm:Kim1}
K.~Kim and J.~L. Nazareth.
\newblock The decomposition principle and algorithms for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:119--133, 1991.

\bibitem{ipm:Kim2}
K.~Kim and J.~L. Nazareth.
\newblock Implementation of a primal null--space affine scaling method and its
  extensions.
\newblock {Technical Report} 92--1, Department of Pure and Applied Mathematics,
  Washington State University, Pullman, WA~99164--3113, USA, January 1992.

\bibitem{ipm:Kim4}
K.~Kim and J.~L. Nazareth.
\newblock A primal null--space affine scaling method.
\newblock {\em ACM Transactions on Mathematical Software}, 20:373--392, 1994.

\bibitem{ipm:Kiwiel2}
K.~C. Kiwiel.
\newblock Complexity of some cutting plane methods that use analytic centers.
\newblock {\em Mathematical Programming}, 74:47--54, 1996.

\bibitem{ipm:Kiwiel1}
K.~C. Kiwiel.
\newblock Efficiency of the analytic center cutting plane method for convex
  minimization.
\newblock {\em SIAM Journal on Optimization}, 1996.

\bibitem{ipm:Klebor1}
S.~Klebor.
\newblock Interior point methods for large scale portfolio optimization.
\newblock Master's thesis, Institute of Mathematics, University of
  G{\"o}ttingen, G{\"o}ttingen, Germany, 1994.

\bibitem{ipm:Klerk9}
{E. de} Klerk.
\newblock {\em Interior point methods for semidefinite programming}.
\newblock PhD thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2600~GA~Delft, The Netherlands, 1997.

\bibitem{ipm:Klerk2}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock A nonconvex weighted potential function for polynomial target
  follwing methods.
\newblock {Technical Report} 95--127, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Klerk1}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Semi--definite problems in truss topology optimization.
\newblock {Technical Report} 95--128, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Klerk3}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Initialization in semidefinite programming via a self--dual
  skew--symmetric embedding.
\newblock {\em Opeartions Research Letters}, 20:213--221, 1997.

\bibitem{ipm:Klerk8}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Primal--dual potential reduction methods for semidefinite programming
  using affine--scaling directions.
\newblock {Technical Report} 97--29, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1997.

\bibitem{ipm:Klerk7}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock A short survey on semidefinite programming.
\newblock In W.~K. Klein~Haneveld et~al., editor, {\em {Ten Years LNMB, Ph.d.
  Research and Graduate Courses of the Dutch Network of Operations Research}},
  volume 122 of {\em CWI Tracts}, pages 323--339. Centrum for Mathematics and
  Informatics (CWI), Amsterdam, The Netherlands, 1997.

\bibitem{ipm:Klerk4}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Infeasible start semidefinite programming algorithms via self--dual
  embeddings.
\newblock In P.~M. Pardalos and H.~Wolkowicz, editors, {\em Topics in
  Semidefinite and Interior--Point Methods}, volume~18 of {\em Fields Institute
  Communications Series}, pages 215--236. American Mathematical Society (AMS),
  Providence, Rhode Island, USA, 1998.

\bibitem{ipm:Klerk5}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock On primal--dual path following algorithms for semidefinite
  programming.
\newblock In F.~Gianessi, S.~Koml{\'o}si, and T.~Rapcs{\'a}k, editors, {\em
  {New Trends in Mathematical Programming}}, pages 137--157. Kluwer Academic
  Publishers, Dordrecht, The Netherlands, 1998.

\bibitem{ipm:Klerk6}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Polynomial primal--dual affine scaling algorithms in semidefinite
  programming.
\newblock {\em Journal of Combinatorial Optimization}, 2:51--69, 1998.

\bibitem{ipm:Kliokys1}
E.~Kliokys, E.~Handschin, and M.~Langer.
\newblock An interior point method for state elimination with current magnitude
  measurements and inequality constraints.
\newblock {\em Power Industry Computer Application Conference (Salt Lake City,
  UT, USA, 1995)}, pages 385--391, 1995.
\newblock See also Handschin et al. \cite{ipm:Handschin1}.

\bibitem{ipm:Knyazev1}
E.~A. Knyazev.
\newblock The method of centers with adaptation of parameters on the basis of
  the steepest descent.
\newblock {\em Issledovaniya po Prikladnoi Matematike (Kazanskii Universitet)},
  15:13--24, 1988.
\newblock (In Russian).

\bibitem{ipm:Koenker1}
R.~W. Koenker and B.-J. Park.
\newblock An interior point algorithm for nonlinear quantile regression.
\newblock {\em Journal of Econometrics}, 71:265--283, 1996.

\bibitem{ipm:Kojima1}
M.~Kojima.
\newblock Determining basic variables of optimal solutions in {Karmarkar's new
  LP} algorithm.
\newblock {\em Algorithmica}, 1(4):499--515, 1986.

\bibitem{ipm:Kojima30}
M.~Kojima.
\newblock A primitive interior--point algorithm for semidefinite programs in
  {Mathematica}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--293, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, December 1994.

\bibitem{ipm:Kojima29}
M.~Kojima.
\newblock Basic lemmas in polynomial--time infeasible--interior--point methods
  for linear programs.
\newblock {\em Annals of Operations Research}, 62:1--28, 1996.

\bibitem{ipm:Kojima39}
M.~Kojima.
\newblock Semidefinite programming and interior--point methods.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--314, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, April
  1996.

\bibitem{ipm:Kojima22}
M.~Kojima and T.~Ishihara.
\newblock On the {$Big~M$} in the affine scaling algorithm.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--255, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, March 1992.

\bibitem{ipm:Kojima32}
M.~Kojima, S.~Kojima, and S.~Hara.
\newblock Linear algebra for semidefinite programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 1004:1--23,
  1997.

\bibitem{ipm:Kojima10}
M.~Kojima, Y.~Kurita, and S.~Mizuno.
\newblock Large--step interior point algorithms for linear complementarity
  problems.
\newblock {\em SIAM Journal on Optimization}, 3(2):398--412, 1993.

\bibitem{ipm:Kojima9}
M.~Kojima and N.~Megiddo.
\newblock The relation between the path of centers and {Smale's} regularization
  of the linear programming problem.
\newblock {\em Linear Algebra and Its Applications}, 152:135--139, 1991.

\bibitem{ipm:Kojima20}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A primal--dual exterior point algorithm for linear programming.
\newblock {Research Report} RJ~8500, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, December 1991.
\newblock See also Kojima, Megiddo and Mizuno\,\cite{ipm:Kojima27}.

\bibitem{ipm:Kojima43}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A {Lagrangian} relaxation method for approximating the analytic
  center of a polytope.
\newblock {Technical Report}, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1992.

\bibitem{ipm:Kojima11}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A general framework of continuation methods for complementarity
  problems.
\newblock {\em Mathematics of Operations Research}, 18:945--963, 1993.

\bibitem{ipm:Kojima27}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A primal--dual infeasible--interior--point algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 61:263--280, 1993.
\newblock See also Kojima, Megiddo and Mizuno\,\cite{ipm:Kojima20}.

\bibitem{ipm:Kojima12}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock Theoretical convergence of large--step--primal--dual interior point
  algorithms for linear programming.
\newblock {\em Mathematical Programming}, 59:1--21, 1993.

\bibitem{ipm:Kojima21}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A conjugate direction method for approximating the analytic center of
  a polytope.
\newblock {\em Journal of Inequalities and Applications}, 2:181--194, 1998.

\bibitem{ipm:Kojima34}
M.~Kojima, N.~Megiddo, S.~Mizuno, and S.~Shindoh.
\newblock Horizontal and vertical decomposition in interior point methods for
  linear programs.
\newblock {Research Report} RJ~9901, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1994.

\bibitem{ipm:Kojima19}
M.~Kojima, N.~Megiddo, S.~Mizuno, and A.~Yoshise.
\newblock An artificial self--dual linear program.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Information Sciences, Tokyo Institute of Technology,
  Oh--Okayama, Meguro--ku, Tokyo~152, Japan, May 1992.
\newblock See Kojima et al.\ \cite{ipm:Kojima14}.

\bibitem{ipm:Kojima17}
M.~Kojima, N.~Megiddo, and T.~Noma.
\newblock Homotopy continuation methods for complementarity problems.
\newblock {Research Report} RJ~6638~(63949), IBM Almaden Research Center, San
  Jose, CA~95120--6099, USA, 1989.

\bibitem{ipm:Kojima18}
M.~Kojima, N.~Megiddo, and T.~Noma.
\newblock Homotopy continuation methods for nonlinear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 16(4):754--774, 1991.

\bibitem{ipm:Kojima8}
M.~Kojima, N.~Megiddo, T.~Noma, and A.~Yoshise.
\newblock {\em {A Unified Approach to Interior Point Algorithms for Linear
  Complementarity Problems}}, volume 538 of {\em Lecture Notes in Computer
  Science}.
\newblock Springer Verlag, Berlin, Germany, 1991.

\bibitem{ipm:Kojima15}
M.~Kojima, N.~Megiddo, T.~Noma, and A.~Yoshise.
\newblock A unified approach to interior point algorithms for linear
  complementarity problems\,: {A} summary.
\newblock {\em Operations Research Letters}, 10:247--254, 1991.

\bibitem{ipm:Kojima3}
M.~Kojima, N.~Megiddo, and Y.~Ye.
\newblock An interior point potential reduction algorithm for the linear
  complementarity problem.
\newblock {\em Mathematical Programming}, 54:267--279, 1992.

\bibitem{ipm:Kojima13}
M.~Kojima, S.~Mizuno, and T.~Noma.
\newblock A new continuation method for complementarity problems with uniform
  {$P$}--functions.
\newblock {\em Mathematical Programming}, 43:107--113, 1989.

\bibitem{ipm:Kojima16}
M.~Kojima, S.~Mizuno, and T.~Noma.
\newblock Limiting behavior of trajectories by a continuation method for
  monotone complementarity problems.
\newblock {\em Mathematics of Operations Research}, 15(4):662--675, 1990.

\bibitem{ipm:Kojima24}
M.~Kojima, S.~Mizuno, and M.~J. Todd.
\newblock Infeasible--interior--point primal--dual potential--reduction
  algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:52--67, 1995.
\newblock See also Mizuno et al.\ \cite{ipm:Mizuno19}.

\bibitem{ipm:Kojima7}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A polynomial--time algorithm for a class of linear complementarity
  problems.
\newblock {\em Mathematical Programming}, 44:1--26, 1989.

\bibitem{ipm:Kojima4}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A primal--dual interior point algorithm for linear programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 29--47. Springer Verlag, New York,
  1989.

\bibitem{ipm:Kojima5}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock Ellipsoids that contain all the solutions of a positive
  semi--definite linear complementarity problems.
\newblock {\em Mathematical Programming}, 48:415--435, 1990.

\bibitem{ipm:Kojima6}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock An ${O(\sqrt{n}L)}$ iteration potential reduction algorithm for
  linear complementarity problems.
\newblock {\em Mathematical Programming}, 50:331--342, 1991.

\bibitem{ipm:Kojima26}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A convex property of monotone complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--267, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, March 1993.

\bibitem{ipm:Kojima14}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A little theorem of the {$Big-M$} in interior point algorithms.
\newblock {\em Mathematical Programming}, 59:361--375, 1993.

\bibitem{ipm:Kojima23}
M.~Kojima, T.~Noma, and M.~Satoh.
\newblock Potential reduction algorithms for monotone complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--251, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, 1992.

\bibitem{ipm:Kojima25}
M.~Kojima, T.~Noma, and A.~Yoshise.
\newblock Global convergence and detecting infeasibility in interior--point
  algorithms.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--257, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, September 1992.
\newblock See also Kojima, Noma and Yoshise \cite{ipm:Kojima28}.

\bibitem{ipm:Kojima28}
M.~Kojima, T.~Noma, and A.~Yoshise.
\newblock Global convergence in infeasible--interior--point algorithms.
\newblock {\em Mathematical Programming}, 65:43--72, 1994.
\newblock See also Kojima, Noma and Yoshise \cite{ipm:Kojima25}.

\bibitem{ipm:Kojima35}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Global and local convergence of predictor--corrector
  infeasible--interior--point algorithms for semidefinite programs.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--305, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, October 1995.

\bibitem{ipm:Kojima38}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock A note on the {Nesterov--Todd} and the {Kojima--Shindoh--Hara} search
  directions in semidefinite programming.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--313, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, April
  1996.

\bibitem{ipm:Kojima37}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock A predictor--corrector interior--point algorithm for the semidefinite
  linear complementarity problem using the {Alizadeh--Haeberly--Overton} search
  direction.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--311, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, January 1996.
\newblock To appear in {\em{SIAM Journal on Optimization}}.

\bibitem{ipm:Kojima31}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Reduction of monotone linear complementarity problems over cones to
  linear programs over cones.
\newblock {\em Acta Mathematica Vietnamica}, 22:147--157, 1997.

\bibitem{ipm:Kojima40}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Search directions in the {SDP} and the monotone {SDLCP}\,:
  {Generalization} and inexact computation.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--327, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March
  1997.

\bibitem{ipm:Kojima36}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Local convergence of predictor--corrector infeasible--interior--point
  algorithms for {SDP}s and {SDLCP}s.
\newblock {\em Mathematical Programming}, 80:129--160, 1998.

\bibitem{ipm:Kojima33}
M.~Kojima, S.~Shindoh, and S.~Hara.
\newblock Interior--point methods for the monotone semidefinite linear
  complementarity problem in symmetric matrices.
\newblock {\em SIAM Journal on Optimization}, 7:86--125, 1997.

\bibitem{ipm:Kojima2}
M.~Kojima and K.~Tone.
\newblock An efficient implementation of {Karmarkar's new LP} algorithm.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--180, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, 1986.

\bibitem{ipm:Kojima41}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Cones of matrices and successive convex relaxations of nonconvex
  sets.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--338, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March
  1998.

\bibitem{ipm:Kojima44}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Discretization and localization in successive convex relaxation
  methods for nonconvex quadratic optimization problems.
\newblock {Research Report} B--341, Department of Mathematical and Computing
  Sciences, Tokyo Institute of Technology, Oh--Okayama, Meguoro, Tokyo\,152,
  Japan, July 1998.
\newblock Also availble as\,: Technical Report COOR\,98--34, Department of
  Combinatorics and Optimization, University of Waterloo, Waterloo,
  Ontario\,N2L\,3G1, Canada.

\bibitem{ipm:Kojima42}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Monotonicity of primal-dual interior-point algorithms for
  semidefinite programming problems.
\newblock {\em Optimization Methods and Software}, 10:275--296, 1998.

\bibitem{ipm:Kolata1}
G.~Kolata.
\newblock A fast way to solve hard problems.
\newblock {\em Science}, 225:1379--1380, September 1984.

\bibitem{ipm:Konno2}
H.~Konno.
\newblock Recent advances in linear programming.
\newblock {\em Journal of the Japan Society of Simulation Technology},
  6(1):18--26, March 1987.
\newblock (In Japanese).

\bibitem{ipm:Konno1}
H.~Konno and Y.~Yajima.
\newblock Path--following algorithms for solving nonconvex programming
  problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Institute of Human and Social Science, Institute of Technology,
  2--12--1~Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, October 1990.

\bibitem{ipm:Kortanek1}
K.~O. Kortanek.
\newblock Vector--supercomputer experiments with the linear programming scaling
  algorithm.
\newblock {Working Paper Series} 87--2, Department of Management Science,
  College of Business Administration, University of Iowa, Iowa City, IA~52240,
  USA, 1987.
\newblock See Kortanek and Zhu \cite{ipm:Kortanek13}, too.

\bibitem{ipm:Kortanek2}
K.~O. Kortanek.
\newblock A second order affine scaling algorithm for the geometric programming
  dual with logarithmic barrier.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Department
  of Management Science, College of Business Administration, University of
  Iowa, Iowa City, IA~52240, USA, August 1990.
\newblock See Kortanek and Ho \cite{ipm:Kortanek7}.

\bibitem{ipm:Kortanek13}
K.~O. Kortanek.
\newblock Vector--supercomputer experiments with the primal affine linear
  programming scaling algorithm.
\newblock {\em SIAM Journal on Scientific Computations}, 14:279--294, 1993.

\bibitem{ipm:Kortanek10}
K.~O. Kortanek and S.~Huang.
\newblock A simultaneous primal--dual potential reduction algorithm for linear
  programming.
\newblock {Working Paper Series} 89--2, Department of Management Science,
  College of Business Administration, University of Iowa, Iowa City, IA~52240,
  USA, 1989.

\bibitem{ipm:Kortanek11}
K.~O. Kortanek and S.~Huang.
\newblock A note on a potential reduction algorithm with simultaneous
  primal/dual updating.
\newblock {\em Operations Research Letters}, 10:501--507, 1992.

\bibitem{ipm:Kortanek9}
K.~O. Kortanek, S.~Huang, and J.~Zhu.
\newblock Central path trajectories and controlled dual perturbations for
  geometric programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Management Science, College of Business Administration,
  University of Iowa, Iowa City, IA~52240, USA, November 1991.

\bibitem{ipm:Kortanek5}
K.~O. Kortanek, D.~N. Leo, and M.~Shi.
\newblock An application of a hybrid algorithm for semi--infinite programming.
\newblock {Talk held at the 12th Symposium on Mathematical Programming,
  Cambridge, MA, USA}, Department of Management Science, College of Business
  Administration, University of Iowa, Iowa City, IA~52240, USA, 1985.

\bibitem{ipm:Kortanek7}
K.~O. Kortanek and H.~No.
\newblock A second order affine scaling algorithm for the geometric programming
  dual with logarithmic barrier.
\newblock {\em Optimization}, 23:303--322, 1992.

\bibitem{ipm:Kortanek6}
K.~O. Kortanek, F.~Potra, and Y.~Ye.
\newblock On some efficient interior point methods for nonlinear convex
  programming.
\newblock {\em Linear Algebra and Its Applications}, 152:169--189, 1991.

\bibitem{ipm:Kortanek3}
K.~O. Kortanek and M.~Shi.
\newblock Convergence results and numerical experiments on a linear programming
  hybrid algorithm.
\newblock {\em European Journal of Operational Research}, 32:47--61, 1987.

\bibitem{ipm:Kortanek14}
K.~O. Kortanek, X.~J. Xu, and Y.~Ye.
\newblock An infeasible interior--point algorithm for solving primal and dual
  geometric programs.
\newblock {\em Mathematical Programming}, 76:155--181, 1997.

\bibitem{ipm:Kortanek4}
K.~O. Kortanek and J.~Zhu.
\newblock New purification algorithms for linear programming.
\newblock {\em Naval Research Logistics Quarterly}, 35:571--583, 1988.

\bibitem{ipm:Kortanek12}
K.~O. Kortanek and J.~Zhu.
\newblock A polynomial barrier algorithm for linearly constrained convex
  programming problems.
\newblock {\em Mathematics of Operations Research}, 18(1):116--127, 1993.

\bibitem{ipm:Kortanek8}
K.~O. Kortanek and J.~Zhu.
\newblock Controlling the parameter in the logarithmic barrier term for convex
  programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 84:117--143,
  1995.

\bibitem{ipm:Korytowski1}
A.~Korytowski.
\newblock Inner search methods for linear programming.
\newblock {\em Zastosowania Matematyki (Warshaw, Poland)}, 20(2):307--327,
  1990.

\bibitem{ipm:Korzak1}
J.~Korzak.
\newblock {\em {Primal--duale pfadfolgende inexacte
  {\"a}u{\ss}ere--Punkte--Verfahren zur L{\"o}sung lineare Optimierungsaufgaben
  (Primal--dual path--following inexact exterior point methods for the solution
  of linear optimization problems}}.
\newblock PhD thesis, Department of Mathematics and Informatics, University of
  Wuppertal, Gauss--Str.20, D--42097 Wuppertal, Germany, 1997.
\newblock (In German).

\bibitem{ipm:Kovacevic1}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Improving the rate of convergence of interior point methods for
  linear programming.
\newblock {\em Mathematical Programming}, 52:467--479, 1991.

\bibitem{ipm:Kovacevic2}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Interior point methods for transportation problems.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, University of Belgrade, Belgrade, Yugoslavia, January
  1992.

\bibitem{ipm:Kovacevic3}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Stabilization of path--following interior point methods for linear
  programming.
\newblock In {\em IX Conference on Applied Mathematics (Budva, 1994)}, pages
  245--258. University of Novi Sad, Novi Sad, Yugoslavia, 1995.

\bibitem{ipm:Kovacevic4}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock A view of interior point methods for linear programming.
\newblock {\em Yugoslavian Journal of Operations Research}, 5:173--193, 1995.

\bibitem{ipm:Kovacevic5}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}} and M.~D. Asi{\'c}.
\newblock An interior point method for transportation problems.
\newblock {\em Facta Universitatis\,: Series Mathematics and Informatics},
  11:157--170, 1996.

\bibitem{ipm:Kozlov1}
A.~Kozlov.
\newblock The {Karmarkar} algorithm\,: {Is} it for real~?
\newblock {\em SIAM News}, 18(6):1, 4, 13, November 1985.

\bibitem{ipm:Kozlov2}
A.~Kozlov and L.~W. Black.
\newblock Berkeley obtains new results with {Karmarkar} algorithm.
\newblock {\em SIAM News}, 19(3):3, 20, May 1986.

\bibitem{ipm:Kranich1}
E.~Kranich.
\newblock Interior point methods for mathematical programming\,: {A}
  bibliography.
\newblock {Discussion Paper} 171, Institute of Economy and Operations Research,
  FernUniversit{\"a}t Hagen, P.O. Box~940, D--5800~Hagen~1, Germany, May 1991.
\newblock Available through {\em netlib}, see Kranich \cite{ipm:Kranich2}.

\bibitem{ipm:Kranich2}
E.~Kranich.
\newblock Interior--point methods bibliography.
\newblock {\em SIAG/OPT Views--and--News, A Forum for the SIAM Activity Group
  on Optimization}, 1:11, 1992.

\bibitem{ipm:Krawczyk1}
R.~Krawczyk.
\newblock {L{\"o}sung des Erf{\"u}llbarkeitsproblems mit der Interior--Point
  Methode (Solution of the satisfiability problem with the interior--point
  method)}.
\newblock Master's thesis, {Mathematisches Institut,
  Heinrich--Heine--Universit{\"a}t D{\"u}sseldorf}, P.O. Box,
  Geb{\"a}ude~25.00, D{\"u}sseldorf, Germany, September 1994.
\newblock (In German).

\bibitem{ipm:Kruk1}
S.~Kruk, M.~Muramatsu, F.~Rendl, R.~J. Vanderbei, and H.~Wolkowicz.
\newblock The {Gauss--Newton} direction in semidefinite programming.
\newblock {Manuscript}, May 1998.

\bibitem{ipm:Kumke1}
S.~O. Kumke.
\newblock On the convergence of a modified barrier function method for convex
  quadratic and linear programming.
\newblock {\em Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik},
  76:485--486, 1996.

\bibitem{ipm:Lagarias1}
J.~C. Lagarias.
\newblock Analytic algorithms for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New Orleans,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA, May 1987.

\bibitem{ipm:Lagarias2}
J.~C. Lagarias.
\newblock The nonlinear geometry of linear programming, {Part\,III}\,:
  {Projective Legrende} transform coordinates and {Hilbert} geometry.
\newblock {\em Transactions of the American Mathematical Society},
  320:193--225, 1990.

\bibitem{ipm:Lagarias4}
J.~C. Lagarias.
\newblock A collinear scaling interpretation of {Karmarkar's} linear
  programming algorithm.
\newblock {\em SIAM Journal on Optimization}, 3:630--636, 1993.

\bibitem{ipm:Lagarias3}
J.~C. Lagarias and M.~J. Todd.
\newblock {\em Mathematical Developments Arising from Linear Programming\,:
  Proceedings of a Joint Summer Research Conference held at Bowdoin College,
  Brunswick, Maine, USA, June/July 1988}, volume 114 of {\em Contemporary
  Mathematics}.
\newblock American Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Lange1}
K.~Lange.
\newblock An adaptive barrier method for convex programming.
\newblock {\em Methods and Applications of Analysis}, 1:392--402, 1994.

\bibitem{ipm:Lanser1}
S.~Lanser.
\newblock Barrier functions for the interior point methods for nonlinear
  programming and their relation to the characteristic function.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics,
  Delft University of Technology, NL--2600 Delft, The Netherlands, 1995.

\bibitem{ipm:Lasdon3}
L.~S. Lasdon.
\newblock An interior point method for nonlinearly constrained problems.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Management Science and Information Systems, College
  of Business Administration, University of Texas at Austin, Austin, TX~78712,
  USA, May 1992.

\bibitem{ipm:Lasdon4}
L.~S. Lasdon, J.~Plummer, and G.~Yu.
\newblock Primal--dual and primal interior point algorithms for general
  nonlinear programs.
\newblock {\em ORSA Journal on Computing}, 7:321--332, 1995.

\bibitem{ipm:Lasdon1}
L.~S. Lasdon, J.~C. Plummer, and G.~Yu.
\newblock An interior point algorithm for general nonlinear programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Management Science and Information Systems, College of
  Business Administration, University of Texas at Austin, Austin, TX~78712,
  USA, November 1991.

\bibitem{ipm:Lasdon2}
L.~S. Lasdon, J.~C. Plummer, and G.~Yu.
\newblock An interior point algorithm for general nonlinear programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Management Science and Information Systems, College of
  Business Administration, University of Texas at Austin, Austin, TX~78712,
  USA, April 1992.

\bibitem{ipm:Lawler1}
E.~L. Lawler.
\newblock Is {Karmarkar's} algorithm for real\,?
\newblock {Talk held at the EURO VII Congress on Operations Research in
  Bologna, Italy}, University of California, Berkeley, CA~94720, USA, June
  1985.

\bibitem{ipm:Lebret1}
H.~Lebret.
\newblock Optimal beamforming via interior point methods.
\newblock {\em Journal of VLSI Signal Processing}, 14:29--41, 1996.

\bibitem{ipm:Lee3}
E.~K. Lee.
\newblock Computational experience of an interior point algorithm in a parallel
  branch--and--cut framework.
\newblock {\em Proceedings of the Eighth SIAM Conference on Parallel Processing
  for Scientific Computing}, page 8pp. (electronic), 1997.

\bibitem{ipm:Lee2}
E.~K. Lee.
\newblock Solving mixed integer nonlinear programming problems using an
  interior point method.
\newblock {RPI Mathematical Report}, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, May 1997.

\bibitem{ipm:Lee4}
E.~K. Lee and J.~E. Mitchell.
\newblock Computational experience of an interior--point {SQP} algorithm in a
  parallel branch--and--bound framework.
\newblock {Technical Report} LEC~97--08, School of Industrial and Systems
  Engineering, Georgia Technology Institute, Atlanta, GA~30322--0205, USA,
  September 1997.

\bibitem{ipm:Lee1}
J.-H. Lee and C.-K. Chen.
\newblock Minimax design of two--dimensional {FIR} digital filters by using an
  interior--point algorithm.
\newblock {\em IEEE International Symposium on Circuits and Systems},
  1:894--897, 1993.

\bibitem{ipm:Lehmkuhl1}
L.~Lehmkuhl.
\newblock {\em A polynomial primal--dual interior point method for convex
  programming with quadratic constraints}.
\newblock PhD thesis, School of Engineering and Applied Science, Department of
  Operations Research, The George Washington University, Washington,
  D.C.~20052, USA, 1993.

\bibitem{ipm:Leibfritz1}
F.~Leibfritz and E.~W. Sachs.
\newblock Numerical solution of parabolic state constrained control problems
  using {SQP}-- and interior--point--methods.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 245--258.
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Leibfritz2}
F.~Leibfritz and E.~W. Sachs.
\newblock Inexact {SQP} interior point methods and large scale optimal control
  problems.
\newblock {Forschungsbericht} 96--6, Institut f{\"u}r Mathematik und
  Informatik, Universit{\"a}t Trier, Trier, Germany, 1996.

\bibitem{ipm:Lely1}
{W. van der} Lely.
\newblock {BIN\,:\,A binary integer programming code using interior--point
  methods}.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2628~CD~Delft, The Netherlands, June 1993.

\bibitem{ipm:Lemmon1}
M.~D. Lemmon, P.~T. Szymanski, and C.~Bett.
\newblock Interior--point competitive learning of control agents in
  colony--style systems.
\newblock {\em Proceedings of the SPIE (The International Society for Optical
  Engineering}, pages 426--, 1995.

\bibitem{ipm:Levkovitz3}
R.~Levkovitz.
\newblock {\em An investigation of the interior point method for large scale
  programming\,:\,{Theory} and computational algorithms}.
\newblock PhD thesis, Mathematics Department, Brunel University, Uxbridge
  MDDX~UB8~3PH, United Kingdom, October 1992.

\bibitem{ipm:Levkovitz2}
R.~Levkovitz, J.~A. Andersen, and G.~Mitra.
\newblock The interior point method for {LP} on parallel computers.
\newblock In P.~Kall, editor, {\em System Modelling and Optimization
  (Proceedings of the 15th IFIP Conference held at the University of Zurich
  1991)}, volume 180 of {\em Lecture Notes in Control and Information
  Sciences}, pages 241--250. Springer Verlag, Berlin, Germany, 1992.

\bibitem{ipm:Levkovitz5}
R.~Levkovitz and G.~Mitra.
\newblock Solution of large sparse symmetric equations on a transputer network.
\newblock In T.~S. Durrani, editor, {\em Proceedings of the 3rd International
  Conference on Applications of Transputers}, pages 105--110. IOS Press,
  Amsterdam, The Netherlands, 1991.

\bibitem{ipm:Levkovitz6}
R.~Levkovitz and G.~Mitra.
\newblock Cholesky factorization of sparse symmetric positive definite matrices
  on distributed parallel computers.
\newblock In G.~L. Reijns and J.~Luo, editors, {\em Transputing in Numerical
  and Neural Network Applications}, pages 30--47. IOS Press, Amsterdam, The
  Netherlands, 1992.

\bibitem{ipm:Levkovitz7}
R.~Levkovitz and G.~Mitra.
\newblock Solution of large--scale linear programs\,: {A} review of hardware,
  software and algorithmic issues.
\newblock In T.~Ciriani and R.~C. Leachman, editors, {\em Optimization in
  Industry\,: Mathematical Programming and Modeling Techniques in Practice},
  pages 139--171. John Wiley \& Sons, New York, NY, USA, 1993.

\bibitem{ipm:Levkovitz8}
R.~Levkovitz and G.~Mitra.
\newblock Experimental investigations in combining primal--dual interior--point
  method and simplex based {LP} solvers.
\newblock {\em Annals of Operations Research}, 58:19--38, 1995.

\bibitem{ipm:Levkovitz1}
R.~Levkovitz, G.~Mitra, and M.~Tamiz.
\newblock Integration of the interior point method within simplex\,:
  {Experiments} in feasible basis recovery.
\newblock {Technical Report}, Department of Mathematics and Statistics, Brunel
  University, Uxbridge, Middlesex~UB8~3PH, United Kingdom, 1991.

\bibitem{ipm:Levkovitz4}
R.~Levkovitz, G.~Mitra, and M.~Tamiz.
\newblock Experimental investigations in combining {IPM} and {Simplex} based
  {LP} solvers.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 353--373. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Lewis1}
A.~S. Lewis and M.~L. Overton.
\newblock Eigenvalue optimization.
\newblock {\em Acta Numerica}, pages 149--190, 1996.

\bibitem{ipm:Lewis2}
A.~S. Lewis and A.~B. Philpott.
\newblock Experiments with affine scaling and semi--infinite programming.
\newblock {\em New Zealand Journal of Mathematics}, 24(2):49--71, 1995.

\bibitem{ipm:Li1}
G.~Li and I.~J. Lustig.
\newblock An implementation of a parallel interior point method for
  multicommodity flow problems.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Mathematical Sciences, Rice University, Houston,
  TX~77251, USA, May 1992.

\bibitem{ipm:Li3}
K.-F. Li and H.-C. Liu.
\newblock An efficient algorithm for solving {LP} problems.
\newblock {\em Chinese Journal of Mathematics}, 24:167--175, 1996.

\bibitem{ipm:Li4}
X.-Q. Li and Q.-Y. Miao.
\newblock An infeasible interior point algorithm for convex quadratic
  programming problems.
\newblock {\em ?}, ?:?, ?
\newblock Found in CMP (1998), p. 283!

\bibitem{ipm:Li2}
Y.~Li.
\newblock A globally convergent method for {$l_{p}$} problems.
\newblock {\em SIAM Journal on Optimization}, 3:609--629, 1993.

\bibitem{ipm:Liao1}
A.~P. Liao.
\newblock {\em Algorithms for linear programming via weighted centers}.
\newblock PhD thesis, School of Operations Research and Industrial Engineering,
  Cornell University, Ithaca, NY~14853--3801, USA, January 1992.

\bibitem{ipm:Liao2}
A.~P. Liao.
\newblock Some variants of {Todd's} low--complexity algorithm.
\newblock {\em Journal on Optimization Theory and Applications}, 86:173--190,
  1995.

\bibitem{ipm:Liao3}
A.~P. Liao and M.~J. Todd.
\newblock Solving {LP} problems via weighted centers.
\newblock {\em SIAM Journal on Optimization}, 6:933--960, 1996.

\bibitem{ipm:Lieu1}
B.~Lieu and P.~HUard.
\newblock La methode des centres dans un espace topolique.
\newblock {\em Numerische Mathematik}, 8:56--67, 1966.

\bibitem{ipm:Lin1}
C.-J. Lin.
\newblock A dual affine scaling based algorithm for solving linear
  semi--infinite programming problems.
\newblock {OR Research Report} 269, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, July 1993.
\newblock See also C.--J. Lin, S.--C. Fang and S.--Y. Wu \cite{ipm:Lin2}.

\bibitem{ipm:Lin2}
C.-J. Lin, S.-C. Fang, and S.-Y. Wu.
\newblock A dual affine scaling based algorithm for solving linear
  semi--infinite programming problems.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 217--234. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Lin5}
C.-J. Lin and R.~Saigal.
\newblock An infeasible start predictor--corrector method for semidefinite
  linear programming.
\newblock {Technical Report}, Department of Industrial and Operational
  Engineering, University of Michigan, Ann Arbor, MI~48109--2117, USA, 1995.

\bibitem{ipm:Lin3}
C.-J. Lin and R.~Saigal.
\newblock A predictor--corrector method for semidefinite linear programming.
\newblock {Technical Report}, Department of Industrial and Operational
  Engineering, University of Michigan, Ann Arbor, MI~48109--2117, USA, October
  1995.
\newblock Revised December 1995.

\bibitem{ipm:Lin8}
C.-J. Lin and R.~Saigal.
\newblock On solving large--scale semidefinite programming problems\,: {A} case
  study of quadratic assignment problem.
\newblock {Technical Report}, Department of Industrial and Operational
  Engineering, University of Michigan, Ann Arbor, MI~48109--2117, USA, December
  1997.

\bibitem{ipm:Lin4}
C.-Y. Lin and M.~K.~H. Fan.
\newblock Convergence analysis of an interior point method in convex
  programming, regular constraint case.
\newblock {\em Proceedings of the 34th Conference on Decision and Control},
  Part 2/4:1103--1108, 1995.

\bibitem{ipm:Lin6}
Z.~Lin, Y.~Lin, and B.~Yu.
\newblock A combined homotopy interior point method for general nonlinear
  programming problems.
\newblock {\em Applied Mathematics and Computation}, 80:209--224, 1996.

\bibitem{ipm:Lin7}
Z.~Lin, B.~Yu, and G.~Feng.
\newblock A combined homotopy interior point method for convex nonlinear
  programming.
\newblock {\em Applied Mathematics and Computation}, 84:193--211, 1997.

\bibitem{ipm:Lindfield1}
G.~R. Lindfield and A.~Salhi.
\newblock A comparative study of the performance and implementation of the
  {Karmarkar} algorithm.
\newblock {Talk held at the Martin Beale Memorial Symposium in London, United
  Kindom}, Department of Computer Science and Applied Mathematics, Aston
  University, Birmingham B4~7ET, United Kingdom, July 1987.

\bibitem{ipm:Ling1}
P.~D. Ling.
\newblock A new proof for the new primal--dual affine scaling interior--point
  algorithm of {Jansen, Roos and Terlaky}.
\newblock {Technical Report} SYS--C93--09, School of Information Systems,
  University of East--Anglia, Norwich, Great Britain, 1993.

\bibitem{ipm:Ling2}
P.~D. Ling.
\newblock A predictor--vcorrector algorithm.
\newblock {Working Paper}, School of Information Systems, University of
  East--Anglia, Norwich, Great Britain, 1993.

\bibitem{ipm:Lisser6}
A.~Lisser.
\newblock {\em Un logiciel derive de l'algorithme de {Karmarkar} pour la
  resolution de programmes lineaires de grande taille {(A computational
  derivation of Karmarkar's algorithm for the solution of large--scaled linear
  programs)}}.
\newblock PhD thesis, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1987.
\newblock (In French).

\bibitem{ipm:Lisser4}
A.~Lisser and M.~J. Chifflet.
\newblock A comparison of projective and affine approaches in interior point
  methods.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Centre National d'Etudes des Telecommunications, PAA--ATR,
  38--40~Rue du General--Leclerc, F--92131~Issy--Les--Moulineaux, France, July
  1991.

\bibitem{ipm:Lisser2}
A.~Lisser, N.~Maculan, and M.~Minoux.
\newblock Approximate one--dimensional minimization of the potential function
  improves the convergence speed of {Karmarkar's} method.
\newblock {Unpublished Manuscript}, Laboratoire de Analyse et Modelisation de
  Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1985.

\bibitem{ipm:Lisser3}
A.~Lisser, N.~Maculan, and M.~Minoux.
\newblock Large steps preserving polynomiality in {Karmarkar's} algorithm.
\newblock Cahier~77, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1987.

\bibitem{ipm:Lisser5}
A.~Lisser and P.Tolla.
\newblock An efficient software using the {Karmarkar's} algorithm.
\newblock {Talk held at the EURO/TIMS Joint International Conference on
  Operational Research in Paris, France}, Laboratoire de Analyse et
  Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de
  Paris Dauphine, F--75775~Paris~Cedex~16, France, July 1988.

\bibitem{ipm:Lisser1}
A.~Lisser and P.~Tolla.
\newblock Variants of {Karmarkar's} algorithm.
\newblock {\em Electricite de France (EDF) Bulletin de la Direction des Etudes
  et Recherches Serie C Mathematique, Informatique (Paris)}, 3:21--36, 1989.

\bibitem{ipm:Litvinchev1}
I.~S. Litvinchev.
\newblock The application of lower bounds for minimization by the interior
  point method.
\newblock {\em Zhurnal Vchyislitelnoi Matematiki i Matematicheskoi Fiziki
  (Nauk, Moscow)}, 34:978--983, 1994.
\newblock (In Russian). Translated in\,: {\em Computational Mathematics and
  Mathematical Physics 34 (1994):\,843--847}.

\bibitem{ipm:Liu1}
S.~Liu.
\newblock A long step path--following algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, May 1990.

\bibitem{ipm:Liu3}
S.~Liu.
\newblock {\em Interior point methods for linear, convex quadratic, and convex
  programming}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Research, Columbia University, New York, NY~10027, USA, 1991.

\bibitem{ipm:Liu2}
S.~Liu and D.~Goldfarb.
\newblock Interior point potential function reduction algorithms for solving
  convex quadratic programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, October 1989.
\newblock See Goldfarb and Liu \cite{ipm:Goldfarb10}.

\bibitem{ipm:Lootsma1}
F.~A. Lootsma.
\newblock {\em Numerical Methods for Nonlinear Optimization}.
\newblock Academic Press, London, United Kingdom, 1972.

\bibitem{ipm:Lord1}
E.~A. Lord, V.~C. Venkaiah, and S.~K. Sen.
\newblock Solution of linear programming problems by a centering algorithm.
\newblock {\em Proceedings of the CSI--91}, pages 433--439, 1991.

\bibitem{ipm:Lord2}
E.~A. Lord, V.~C. Venkaiah, and S.~K. Sen.
\newblock A shrinking polytope method for linear programming.
\newblock {\em Neural Parallel Scientific Computing}, 4:325--339, 1996.

\bibitem{ipm:Loute1}
E.~Loute and J.-Ph. Vial.
\newblock A parallelisable block {Cholesky} factorization for staircase linear
  programming problems.
\newblock {CORE Discussion Paper} 9260, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, 1992.

\bibitem{ipm:Lu1}
C.~N. Lu and M.~R. Unum.
\newblock Network constrained security control using an interior point
  algorithm.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 8:1068--1076, 1993.

\bibitem{ipm:Lu2}
X.-M. Lu.
\newblock A simplex--interior point algorithm for solving linear programming
  problems.
\newblock {\em Journal on Systems Science and Mathematical Sciences},
  16:211--227, 1996.

\bibitem{ipm:Lu3}
X.-M. Lu, Y.~Ye, and F.~Wu.
\newblock A generalized predictor--corrector linear programming algorithm.
\newblock {\em Mathematica Numerica Sinica}, 17:271--281, 1995.
\newblock (In Chinese, English summary).

\bibitem{ipm:Luo1}
J.~Luo and G.~L. Reijns.
\newblock Parallel solution of the revised simplex method and interior point
  methods for linear programming.
\newblock In {\em Proceedings of the 1991 International Symposium in Side,
  Turkey, October 1991}, volume~VI of {\em Computer and Information Sciences},
  pages 723--736. Elsevier North Holland, Amsterdam, The Netherlands, 1991.

\bibitem{ipm:Luo7}
J.~Luo and G.~L. Reijns.
\newblock Parallel implementation of two algorithms to solve linear programming
  problems.
\newblock In G.~L. Reijns and J.~Luo, editors, {\em Transputing in Numerical
  and Neural Networks Applications}, pages 48--65. IOS Press, Amsterdam, The
  Netherlands, 1992.

\bibitem{ipm:Luo6}
J.~Luo and G.~L. Reijns.
\newblock Solving linear programming problems on transputers.
\newblock volume~5 of {\em Transputer Research and Applications}, pages 70--80.
  IOS Press, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:Luo4}
Z.-Q. Luo.
\newblock Convergence analysis of a primal--dual interior point algorithm for
  convex quadratic programs.
\newblock In R.~P. Agarwal, editor, {\em Recent Trends in Optimization Theory
  and Applications}, volume~5 of {\em World Science Series in Applied
  Analysis}, pages 255--270. World Science Publishing, River Edge, NJ, USA,
  1995.

\bibitem{ipm:Luo5}
Z.-Q. Luo.
\newblock Analysis of a cutting plane method that uses weighted analytic center
  and multiple cuts.
\newblock {\em SIAM Journal on Optimization}, 7:697--716, 1997.

\bibitem{ipm:Luo11}
Z.-Q. Luo, C.~Roos, and T.~Terlaky.
\newblock Complexity analysis of a logarithmic barrier decomposition method for
  semi--infinite linear programming.
\newblock {Technical Report} 97--34, Faculty of Mathematics and Computer
  Science, Technical University of Delft,, NL--2600~GA~Delft, THe Netherlands,
  1995.

\bibitem{ipm:Luo10}
Z.-Q. Luo, J.~F. Sturm, and S.~Zhang.
\newblock Duality and self--duality for conic convex programming.
\newblock {Technical Report} 9620/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, THe Netherlands, 1996.

\bibitem{ipm:Luo12}
Z.-Q. Luo, J.~F. Sturm, and S.~Zhang.
\newblock Duality results for conic convex programming.
\newblock {Technical Report} 9719/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, THe Netherlands, 1997.

\bibitem{ipm:Luo9}
Z.-Q. Luo, J.~F. Sturm, and S.~Zhang.
\newblock Superlinear convergence of a symmetric primal-dual path--following
  algorithm for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:59--81, 1998.

\bibitem{ipm:Luo13}
Z.-Q. Luo and J.~Sun.
\newblock Cutting surfaces and analytic center\,: {A} polynomial algorithm for
  the convex feasibility problem defined by self--concordant inequalities.
\newblock {Technical Report}, Economic Institute, Erasmus University Rotterdam,
  NL--3000~DR~Rotterdam, THe Netherlands, June 1996.

\bibitem{ipm:Luo8}
Z.-Q. Luo and J.~Sun.
\newblock An analytic center based column generation algorithm for convex
  quadratic feasibility problems.
\newblock {\em SIAM Journal on Optimization}, 9:217--235, 1999.

\bibitem{ipm:Luo2}
Z.-Q. Luo and S.~Q. Wu.
\newblock A modified predictor--corrector method for linear programming.
\newblock {\em Computational Optimization and Applications}, 3:83--91, 1994.

\bibitem{ipm:Luo14}
Z.-Q. Luo, S.-Q. Wu, and Y.~Ye.
\newblock Predictor--corrector method for nonlinear complementarity problem.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
  13:321--328, 1997.

\bibitem{ipm:Luo3}
Z.-Q. Luo and Y.~Ye.
\newblock A genuine quadratically convergent polynomial interior point
  algorithm for linear programming.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 235--246. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Luss1}
H.~Luss.
\newblock Optimization\,: {Methodolgy}, algorithms and applications.
\newblock {\em AT~\&~T Technical Journal}, 68:3--6, 1989.

\bibitem{ipm:Lustig1}
I.~J. Lustig.
\newblock A practical approach to {Karmarkar's} algorithm.
\newblock {Technical Report} SOL~85--5, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, June 1985.

\bibitem{ipm:Lustig4}
I.~J. Lustig.
\newblock An experimental analysis of the convergence rate of an interior point
  algorithm.
\newblock {Technical Report} SOR~88--5, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, March 1988.

\bibitem{ipm:Lustig3}
I.~J. Lustig.
\newblock A generic primal--dual interior point algorithm.
\newblock {Technical Report} SOR~88--3, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1988.

\bibitem{ipm:Lustig2}
I.~J. Lustig.
\newblock Identifying an optimal basis of a linear program using an interior
  point method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, School of Engineering and Applied Science, Department of Civil
  Engineering and Operations Research, Princeton University, Princeton,
  NJ~08544, USA, April 1988.

\bibitem{ipm:Lustig6}
I.~J. Lustig.
\newblock An analysis of an available set of linear programming test problems.
\newblock {\em Computers and Operations Research}, 16:173--184, 1989.
\newblock Augmented version in the Technical Report SOL~87-11, Systems
  Optimization Laboratory, Department of Operations Research, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Lustig17}
I.~J. Lustig.
\newblock Phase\,1 search directions for a primal--dual interior point method
  for linear programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 121--130. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Lustig5}
I.~J. Lustig.
\newblock Feasibility issues in aprimal--dual interior point method for linear
  programming.
\newblock {\em Mathematical Programming}, 49:145--162, 1990/91.

\bibitem{ipm:Lustig13}
I.~J. Lustig.
\newblock An implementation of a strongly polynomial time algorithm for basis
  recovery.
\newblock {Technical Report} (in preparation), School of Engineering and
  Applied Science, Department of Civil Engineering and Operations Research,
  Princeton University, Princeton, NJ~08544, USA, 1991.

\bibitem{ipm:Lustig21}
I.~J. Lustig and G.~Y. Li.
\newblock An implementation of a parallel primal--dual interior point method
  for block--structured linear programs.
\newblock {\em Computational Optimization and Applications}, 1:141--161, 1992.

\bibitem{ipm:Lustig12}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock The primal--dual interior point method on the {C}ray supercomputer.
\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
  Optimization, Papers from the Workshop held at Cornell University, Ithaca,
  NY, USA, October 1989}, volume~46 of {\em SIAM Proceedings in Applied
  Mathematics}, pages 70--80. Society of Industrial and Applied Mathematics
  (SIAM), Philadelphia, PA, USA, 1990.

\bibitem{ipm:Lustig8}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Recent computational experience with the primal--dual interior point
  method for linear programming.
\newblock {Technical Report} RRR~46--89, RUTCOR Center of Operations Research,
  Rutgers University, New Brunswick, NJ~08903, USA, 1990.
\newblock Incorrect citation, elsewhere; see Lustig et al.\,\cite{ipm:Lustig7}.

\bibitem{ipm:Lustig15}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Starting and restarting the primal--dual interior point method.
\newblock {Technical Report} SOR~90--14, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1990.
\newblock Also available as\,: Rutgers Research Report 61--90, Rutgers
  University, New Brunswick, NJ, USA.

\bibitem{ipm:Lustig7}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Computational experience with a primal--dual interior point method
  for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:191--222, 1991.

\bibitem{ipm:Lustig18}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Interior method vs. simplex method\,: {Beyond {\tt netlib}}.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:41--44, August 1991.

\bibitem{ipm:Lustig11}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Recent advances in the {OB1} interior point code.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, School of Engineering and Applied Science, Department of
  Civil Engineering and Operations Research, Princeton University, Princeton,
  NJ~08544, USA, May 1991.
\newblock See Bixby et al.\ \cite{ipm:Bixby1}.

\bibitem{ipm:Lustig16}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock The interaction of algorithms and architectures for interior point
  methods.
\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
  Computing}, pages 190--205. North--Holland, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:Lustig14}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock On implementing {Mehrotra's} predictor--corrector interior point
  method for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:435--449, 1992.

\bibitem{ipm:Lustig19}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Computational experience with a globally convergent primal--dual
  predictor--corrector algorithm for linear programming.
\newblock {\em Mathematical Programming}, 66:123--135, 1994.

\bibitem{ipm:Lustig20}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Interior point methods for linear programming\,: {Computational}
  state of the art.
\newblock {\em ORSA Journal on Computing}, 6:1--14, 1994.

\bibitem{ipm:Lustig22}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock The last word on interior point methods for linear programming---for
  now.
\newblock {\em ORSA Journal on Computing}, 6:35--36, 1994.

\bibitem{ipm:Lustig9}
I.~J. Lustig, J.~M. Mulvey, and T.~J. Carpenter.
\newblock The formulation of stochastic programs for interior point methods.
\newblock {\em Operations Research}, 39(5):757--770, 1991.

\bibitem{ipm:Lustig23}
I.~J. Lustig and E.~Rothberg.
\newblock Gigaflops in linear programming.
\newblock {\em Operations Research Letters}, 18:157--165, 1996.

\bibitem{ipm:Lustig10}
I.~J. Lustig, D.~F. Shanno, and J.~W. Gregory.
\newblock The primal--dual interior point method on a {C}ray supercomputer.
\newblock {Technical Report} SOR~89--21, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1989.
\newblock Same as Lustig et al.\ \cite{ipm:Lustig12}.

\bibitem{ipm:Luethi1}
H.-J. L{\"u}thi and B.~B{\"u}eler.
\newblock The analytic center quadratic cut method {(ACQCM)} for strongly
  monotone variational inequality problems.
\newblock {Technical Report}, Institute of Operations Research,
  Eidgen{\"o}ssische Technische Hochschule (ETH) Z{\"u}rich, Z{\"u}rich, The
  Switzerland, March 1998.

\bibitem{ipm:Ma1}
Z.~Ma.
\newblock On interior point algorithms for linear programming.
\newblock {\em Advanced Mathematics (Beijing, China)}, 21(3):274--288, 1992.
\newblock (In Chinese\,?).

\bibitem{ipm:Maaren1}
{H. van} Maaren and T.~Terlaky.
\newblock Inverse barriers and {CES}--functions in linear programming.
\newblock {\em Operations Research Letters}, 20, 1997.

\bibitem{ipm:Madrigal1}
M.~Madrigal and Q.~H. Quintana.
\newblock Optimal day--ahead network--constrained power system's market
  operations planning using an interior--point method.
\newblock {\em Proceedings of the 11th Canadian Conference on Electrical and
  Computer Engineering}, Part\,1/2, 1998.

\bibitem{ipm:Mahony1}
R.~E. Mahony and J.~B. Moore.
\newblock Recursive interior--point linear programming algorithm based on
  {Lie--Brockett} flows.
\newblock In K.~H. Phua, C.~M. Wang, W.~Y. Yeong, T.~Y. Leong, H.~T. Loh, K.~C.
  Tan, and F.~S. Chou, editors, {\em Optimization\,: Techniques and
  Applications, Vol.\,1 (Proceedings of the International Conference (ICOTA)
  held in Singapore 1992)}, pages 21--29. World Science Publishing, River Edge,
  NJ, USA, 1992.

\bibitem{ipm:Maier1}
S.~Maier.
\newblock {Primal--duales innere--Punkte--Verfahren mit endlicher Genauigkeit
  zur L{\"o}sung linearer Programme (A primal--dual interior point method with
  finite accuracy for solving linear programs)}.
\newblock Master's thesis, Institut f{\"u}r Mathematik der
  Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Augsburg,
  D--8900~Augsburg, Germany, 1989.
\newblock (In German).

\bibitem{ipm:Man1}
H.~Man.
\newblock The effect of centering in an interior point algorithm.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2628~CD~Delft, The Netherlands, 1993.

\bibitem{ipm:Mangasarian1}
O.~L. Mangasarian and R.~Setiono.
\newblock Serial and parallel interior proximal point methods for linear
  programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Computer Science, University of Wisconsin, Madison,
  WI~53706, USA, May 1990.

\bibitem{ipm:Marcarenhas2}
W.~F. Marcarenhas.
\newblock New proofs of cobvergence for the dual affine scaling algorithm.
\newblock {Research Report}, Universidade Estadural de Campinas, Campinas~S.
  P., Brazil, 1993.

\bibitem{ipm:Marcarenhas1}
W.~F. Marcarenhas.
\newblock The affine scaling algorithm fails for stepsize 0.999.
\newblock {\em SIAM Journal on Optimization}, 7:34--46, 1997.

\bibitem{ipm:Margraff1}
G.~Margraff.
\newblock {Analyse und Modifikation des Karmarkar Verfahrens (Analysis and
  modification of Karmarkar's algorithm)}.
\newblock Master's thesis, Universit{\"a}t Trier, Fachbereich~IV,
  D--5500~Trier, Germany, 1987.
\newblock (In German).

\bibitem{ipm:Maros1}
I.~Maros and C.~M{\'e}sz{\'a}ros.
\newblock The role of the augmented system in interior point methods.
\newblock {\em European Journal of Operational Research}, 107:720--736, 1998.

\bibitem{ipm:Marsten7}
R.~E. Marsten.
\newblock The {IMP System} on personal computers.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
  USA}, Department of MIS, University of Arizona, Tucson, AZ~85721, USA,
  October 1987.

\bibitem{ipm:Marsten8}
R.~E. Marsten.
\newblock Interior point methods for large scale linear programming.
\newblock {Talk held at the Second International Conference on Industrial and
  Applied Mathematics (ICIAM~'91), Washington, DC, USA}, School of Industrial
  and Systems Engineering, Georgia Technology Institute, Atlanta,
  GA~30322--0205, USA, July 1991.

\bibitem{ipm:Marsten1}
R.~E. Marsten and M.~J. Saltzman.
\newblock A dual--affine interior point algorithm for {LP's} with bounded
  variables.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, Department of MIS, University of Arizona, Tucson, AZ~85721, USA,
  October 1988.
\newblock See Marsten et al.\ \cite{ipm:Marsten5}.

\bibitem{ipm:Marsten4}
R.~E. Marsten, M.~J. Saltzman, J.~W. Gregory, T.~G. Hewitt, and D.~F. Shanno.
\newblock The dual affine interior point method for linear programming
  implementation on {Cray} supercomputers.
\newblock {Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver,
  British Columbia, Canada}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30322--0205, USA, May 1989.

\bibitem{ipm:Marsten10}
R.~E. Marsten, M.~J. Saltzman, and D.~F. Shanno.
\newblock A dual affine interior point algorithm for {LP} with bounded
  varaibles.
\newblock {Talk held at the XIII International Symposium on Mathematical
  Programming in Tokyo, Japan}, School of Industrial and System Engineering,
  Georgia Institute of Technology, Atlanta, GA~30322, USA, August 1988.
\newblock See Marsten et al.\ \cite{ipm:Marsten5}.

\bibitem{ipm:Marsten5}
R.~E. Marsten, M.~J. Saltzman, D.~F. Shanno, J.~F. Ballintijn, and G.~S.
  Pierce.
\newblock Implementation of a dual affine interior point algorithm for linear
  programming.
\newblock {\em ORSA Journal on Computing}, 1:287--297, 1989.

\bibitem{ipm:Marsten2}
R.~E. Marsten and D.~F. Shanno.
\newblock On implementing {Karmarkar's} algorithm.
\newblock {Technical Report}, Department of MIS, University of Arizona, Tucson,
  AZ~85721, USA, 1985.
\newblock Same as Shanno and Marsten \cite{ipm:Shanno5}.

\bibitem{ipm:Marsten9}
R.~E. Marsten and D.~F. Shanno.
\newblock Interior point methods for linear programming\,: {Ready} for
  production use.
\newblock {Workshop at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, School of Industrial and System Engineering, Georgia Institute of
  Technology, Atlanta, GA~30322, USA, October 1990.

\bibitem{ipm:Marsten3}
R.~E. Marsten and D.~F. Shanno.
\newblock Recent computational experience with the primal--dual interior point
  method.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, School of Industrial and Systems Engineering, Georgia
  Technology Institute, Atlanta, GA~30322--0205, USA, January 1990.

\bibitem{ipm:Marsten11}
R.~E Marsten, D.~F. Shanno, and E.~M. Simantiraki.
\newblock Interior point methods for linear and nonlinear programming.
\newblock In I.~A. Duff and A.~Watson, editors, {\em Numerical Analysis\,: The
  State--of--the--Art}. Institute of Mathematics and its Applications, London,
  Great Britain, 1996.

\bibitem{ipm:Marsten6}
R.~E. Marsten, R.~Subramaniam, M.~J. Saltzman, I.~J. Lustig, and D.~F. Shanno.
\newblock Interior point methods for linear programming\,: {Just call Newton,
  Lagrange, and Fiacco and McCormick\,!}
\newblock {\em Interfaces}, 20(4):105--116, 1990.

\bibitem{ipm:Martinez1}
H.~J. Mart{\'i}nez.
\newblock On motivating the {Mitchell--Todd} modification of {Karmarkar's}
  algorithm for {LP} problems with free variables.
\newblock {\em Journal of Optimization Theory and Applications}, 84:675--679,
  1995.

\bibitem{ipm:Martinez2}
H.~J. Mart{\'i}nez, Z.~Parada, and R.~A. Tapia.
\newblock On the charactarization of {Q}--superlinear convergence of
  quasi--{Newton} interior--point methods for nonlinear programming.
\newblock {\em Boletin de la Sociedad Matematica Mexicana}, 1:137--148, 1995.

\bibitem{ipm:Martinhon1}
C.~Martinhon and C.~C. Gonzaga.
\newblock A unified analysis of affine and projective primal potential
  reduction algorithms for linear programming.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Systems Engineering and Computer Science,
  COPPE Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil,
  July 1991.

\bibitem{ipm:Marxen1}
A.~Marxen.
\newblock Primal barrier methods for linear programming.
\newblock {Technical Report} SOL~89--6, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, June 1989.

\bibitem{ipm:Marxen2}
A.~Marxen.
\newblock {\em Primal barrier methods for linear programming}.
\newblock PhD thesis, Systems Optimization Laboratory, Department of Operations
  Research, Stanford University, Stanford, CA~94305, USA, 1989.

\bibitem{ipm:Mascarenhas1}
W.~F. Mascarenhas.
\newblock The affine scaling algorithm fails for stepsize 0.999.
\newblock {\em SIAM Journal on Optimization}, 7:34--46, 1997.

\bibitem{ipm:Masuzawa1}
K.~Masuzawa, S.~Mizuno, and M.~Mori.
\newblock A polynomial time interior point algorithm for minimum cost flow
  problems.
\newblock {\em Journal of the Operations Research Society of Japan},
  33:157--167, 1990.

\bibitem{ipm:Matstoms1}
P.~Matstoms.
\newblock Sparse linear least squares problems in optimization.
\newblock {\em Computational Optimization and Applications}, 7:89--110, 1997.

\bibitem{ipm:McCormick1}
G.~P. McCormick.
\newblock Miscellaneous results concerning {Karmarkar's} projective method and
  {SUMT}.
\newblock {Manuscript} GWU/IMSE/Serial T--519/87, Institute for Management
  Science and Engineering, The George Washington University, Washington,
  D.C.~20052, USA, 1987.

\bibitem{ipm:McCormick3}
G.~P. McCormick.
\newblock The projective {SUMT} method for convex programming.
\newblock {\em Mathematics of Operations Research}, 14:203--223, 1989.

\bibitem{ipm:McCormick4}
G.~P. McCormick.
\newblock Resolving the {Shell Dual} with a nonlinear primal--dual algorithm.
\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
  Computing}, pages 233--246. North Holland, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:McCormick5}
G.~P. McCormick and A.~Sofer.
\newblock The {big--M} method for interior point feasibility in convex
  optimization.
\newblock {Technical Report} GWU/IMSE/Serial T--538/90, Institute for
  Management Science and Engineering, The George Washington University,
  Washington, D.C.~20052, USA, 1990.

\bibitem{ipm:McCormick2}
S.~T. McCormick and S.~F. Chang.
\newblock Making $aa{^T}$ sparser for interior--point algorithms\,:
  {Complexity} and heuristics.
\newblock {Technical Report}, Faculty of Commerce and Business Administration,
  University of British Columbia, Vancouver, BC~V6T\,1Y8, Canada, 1990.
\newblock In preparation.

\bibitem{ipm:McDiarmid2}
C.~McDiarmid.
\newblock Why {Karmarkar's} method is fast~?
\newblock {Talk held at the EURO/TIMS Joint International Conference on
  Operational Research in Paris, France}, Institute of Economics and
  Statistics, St. Cross Building, Oxford University, Oxford~OX1~3UL, United
  Kingdom, July 1988.

\bibitem{ipm:McDiarmid1}
C.~McDiarmid.
\newblock On the improvement per iteration in {Karmarkar's} method for linear
  programming.
\newblock {\em Mathematical Programming}, 46:299--320, 1990.

\bibitem{ipm:McLinden1}
L.~McLinden.
\newblock The analogue of {Moreau's} proximation theorem, with applications to
  the nonlinear complementarity problem.
\newblock {\em Pacific Journal of Mathematics}, 88:101--161, 1980.

\bibitem{ipm:McQueen1}
J.~F. McQueen.
\newblock Symposium on {Karmarkar's} algorithm and related algorithms for
  linear programming.
\newblock {\em Bulletin of the Institute of Mathematics and Its Applications},
  21:154--155, 1985.

\bibitem{ipm:McShane2}
K.~A. McShane.
\newblock A superlinearly convergent ${O(\sqrt{n}L)}$ iteration primal--dual
  linear programming algorithm.
\newblock Manuscript, U. S. Government, 2537~Villanova Drive, Vienna, Virginia,
  USA, 1991.

\bibitem{ipm:McShane3}
K.~A. McShane.
\newblock {\em Primal--dual interior point algorithms for linear programming
  and the linear comlementarity problem}.
\newblock PhD thesis, School of Operations Research, Cornell University,
  Ithaca, NY~14853--3801, USA, August 1992.

\bibitem{ipm:McShane4}
K.~A. McShane.
\newblock Superlinearly convergent ${O(\sqrt{n}L)}$--iteration interior--point
  algorithms for linear programming and the monotone linear complementary
  problem.
\newblock {\em SIAM Journal on Optimization}, 4:247--261, 1994.

\bibitem{ipm:McShane5}
K.~A. McShane.
\newblock On the superlinear convergence of an $o(n^{3}l)$ interior point
  algorithm for monotone {LCP}.
\newblock {\em SIAM Journal on Optimization}, 6:978--993, 1996.

\bibitem{ipm:McShane1}
K.~A. McShane, C.~L. Monma, and D.~F. Shanno.
\newblock An implementation of a primal--dual interior point method for linear
  programming.
\newblock {\em ORSA Journal on Computing}, 1:70--83, 1989.

\bibitem{ipm:Medina1}
J.~Medina, V.~H. Quintana, A.~J. Conejo, and F.~P. Thoden.
\newblock A comparison of interior--point codes for medium--term hydro--thermal
  coordination.
\newblock In {\em Proceedings of the 20th International Conference on Power
  Industry Computer Applications}, pages 224--231, New York, NY, USA, 1996.
  IEEE Society Press.

\bibitem{ipm:Megiddo1}
N.~Megiddo.
\newblock A variation on {Karmarkar's} algorithm.
\newblock {Preliminary Report}, IBM San Jose Research Laboratory, San Jose,
  CA~95193, USA, 1984.

\bibitem{ipm:Megiddo3}
N.~Megiddo.
\newblock Introduction\,: {New} approaches to linear programming.
\newblock {\em Algorithmica}, 1(4):387--394, 1986.

\bibitem{ipm:Megiddo2}
N.~Megiddo.
\newblock {\em New Approaches to Linear Programming}, volume 1(4) of {\em
  Algorithmica}.
\newblock Springer Verlag, Berlin, Germany, 1986.

\bibitem{ipm:Megiddo4}
N.~Megiddo.
\newblock Linear programming\,(1986).
\newblock {\em Annual Review of Computer Science}, 2:119--145, 1987.

\bibitem{ipm:Megiddo6}
N.~Megiddo.
\newblock On the complexity of linear programming.
\newblock In T.~F. Bewley, editor, {\em Advances in Economic Theory---The Fifth
  World Congress}, volume~12 of {\em Econometric Society Monographs}, pages
  225--258. Cambridge University Press, Cambridge, United Kingdom, 1987.

\bibitem{ipm:Megiddo5}
N.~Megiddo.
\newblock Report on the conference\,: {Progress} in mathematical programming.
\newblock {Technical Report} RJ~5923, IBM~T.~J.~Watson Research Center,
  Yorktown Heights, NY~10598, USA, October 1987.

\bibitem{ipm:Megiddo13}
N.~Megiddo.
\newblock A note on {Karmarkar's} projective transformation.
\newblock {Unpublished Manuscript}, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, December 1988.

\bibitem{ipm:Megiddo8}
N.~Megiddo.
\newblock Switching from a primal--dual {N}ewton algorithm to a primal--dual
  (interior) simplex algorithm.
\newblock {Technical Report} RJ~6327, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1988.

\bibitem{ipm:Megiddo11}
N.~Megiddo.
\newblock Pathways to the optimal set in linear programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 131--158. Springer Verlag, New
  York, 1989.
\newblock Identical version in\,: {\em Proceedings of the 6th Mathematical
  Programming Symposium of Japan, Nagoya, Japan, 1--35, 1986}.

\bibitem{ipm:Megiddo10}
N.~Megiddo.
\newblock {\em Progress in Mathematical Programming\,: Interior Point and
  Related Methods}.
\newblock Springer Verlag, New York, 1989.

\bibitem{ipm:Megiddo7}
N.~Megiddo.
\newblock On solving the linear programming problem approximately.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 35--50. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Megiddo9}
N.~Megiddo.
\newblock On finding primal-- and dual--optimal bases.
\newblock {\em ORSA Journal on Computing}, 3:63--65, 1991.

\bibitem{ipm:Megiddo14}
N.~Megiddo, S.~Mizuno, and T.~Tsuchiya.
\newblock A modified layered--step interior--point algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 82:339--355, 1998.

\bibitem{ipm:Megiddo12}
N.~Megiddo and M.~Shub.
\newblock Boundary behavior of interior point algorithms in linear programming.
\newblock {\em Mathematics of Operations Research}, 14:97--146, 1989.

\bibitem{ipm:Mehrotra1}
S.~Mehrotra.
\newblock A self--correcting version of {Karmarkar's} algorithm.
\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, 1986.

\bibitem{ipm:Mehrotra3}
S.~Mehrotra.
\newblock Implementation of some interior point methods for linear
  programming\,: {Recent} developments.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
  USA}, Department of Industrial Engineering and Management Science,
  Northwestern University, Evanston, IL~60208, USA, October 1987.

\bibitem{ipm:Mehrotra2}
S.~Mehrotra.
\newblock {\em Variants of {Karmarkar's} algorithm\,: {Theoretical} complexity
  and practical implementation}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Reseach, Columbia University, New York, NY~10027, USA, 1987.

\bibitem{ipm:Mehrotra6}
S.~Mehrotra.
\newblock Implementation of affine scaling methods\,: {Towards} faster
  implementations with complete {Cholesky} factor in use.
\newblock {Technical Report} 89--15, Department of Industrial Engineering and
  Management Science, Northwestern University, Evanston, IL~60208, USA, October
  1989.

\bibitem{ipm:Mehrotra4}
S.~Mehrotra.
\newblock On implementation of interior point methods for linear programming\,:
  {Karmarkar's} preconditioners.
\newblock {Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver,
  British Columbia, Canada}, Department of Industrial Engineering and
  Management Science, Northwestern University, Evanston, IL~60208, USA, May
  1989.

\bibitem{ipm:Mehrotra20}
S.~Mehrotra.
\newblock Higher order methods and their performance.
\newblock {Technical Report} TR~90--16R1, Department of Industrial Engineering
  and Management Science, Northwestern University, Evanston, IL~60208, USA,
  1990.
\newblock Revised July 1991.

\bibitem{ipm:Mehrotra9}
S.~Mehrotra.
\newblock Implementations of affine scaling methods\,: {Speeding} up the
  computation.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Industrial Engineering and Management Science,
  Northwestern University, Evanston, IL~60208, USA, May 1990.

\bibitem{ipm:Mehrotra8}
S.~Mehrotra.
\newblock On an implementation of the primal--dual predictor--corrector
  algorithms.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
  Mathematical Programming, Asilomar, CA, USA}, Department of Industrial
  Engineering and Management Science, Northwestern University, Evanston,
  IL~60208, USA, February 1990.

\bibitem{ipm:Mehrotra19}
S.~Mehrotra.
\newblock Finite termination and superlinear convergence in primal--dual
  methods.
\newblock {Technical Report} 91--13, Department of Industrial Engineering and
  Management Science, Northwestern University, Evanston, IL~60208, USA, July
  1991.

\bibitem{ipm:Mehrotra16}
S.~Mehrotra.
\newblock Generalized prediction--corrector methods for solving linear
  programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Industrial Engineering and Management Science,
  Northwestern University, Evanston, IL~60208, USA, May 1991.

\bibitem{ipm:Mehrotra18}
S.~Mehrotra.
\newblock Handling free variables in interior methods.
\newblock {Technical Report} 91--06, Department of Industrial Engineering and
  Management Science, Northwestern University, Evanston, IL~60208, USA, March
  1991.

\bibitem{ipm:Mehrotra17}
S.~Mehrotra.
\newblock Higher--order methods for solving linear programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Industrial Engineering and Management Science,
  Northwestern University, Evanston, IL~60208, USA, May 1991.

\bibitem{ipm:Mehrotra7}
S.~Mehrotra.
\newblock On finding a vertex solution using interior point methods.
\newblock {\em Linear Algebra and Its Applications}, 152:233--253, 1991.

\bibitem{ipm:Mehrotra22}
S.~Mehrotra.
\newblock Deferred rank--one updates in ${O(n^{3}L)}$ interior point algorithm.
\newblock {\em Journal of the Operations Research Society of Japan},
  35:345--352, 1992.

\bibitem{ipm:Mehrotra24}
S.~Mehrotra.
\newblock Finite termination in interior--point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Industrial Engineering and Management Sciences,
  Northwestern University, Evanston, IL~60208, USA, May 1992.

\bibitem{ipm:Mehrotra5}
S.~Mehrotra.
\newblock Implementation of affine scaling methods\,: {Approximate} solutions
  of systems of linear equations using preconditioned conjugate gradient
  methods.
\newblock {\em ORSA Journal on Computing}, 4:103--118, 1992.

\bibitem{ipm:Mehrotra27}
S.~Mehrotra.
\newblock On the implementation of a primal--dual interior point method.
\newblock {\em SIAM Journal on Optimization}, 2(4):575--601, 1992.

\bibitem{ipm:Mehrotra25}
S.~Mehrotra.
\newblock Quadratic convergence in a primal--dual method.
\newblock {\em Mathematics of Operations Research}, 18:741--751, 1993.

\bibitem{ipm:Mehrotra31}
S.~Mehrotra.
\newblock Asymptotic convergence in a generalized predictor--corrector method.
\newblock {\em Mathematical Programming}, 74:11--28, 1996.

\bibitem{ipm:Mehrotra23}
S.~Mehrotra and R.~Fourer.
\newblock Solving symmetric indefinite systems in interior point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Industrial Engineering and Management Sciences,
  Northwestern University, Evanston, IL~60208, USA, May 1992.

\bibitem{ipm:Mehrotra26}
S.~Mehrotra and R.~D.~C. Monteiro.
\newblock Parametric and range analysis for interior point methods.
\newblock {Technical Report}, Department of Systems and Industrial Engineering,
  University of Arizona, Tucson, AZ~85721, USA, April 1992.

\bibitem{ipm:Mehrotra29}
S.~Mehrotra and R.~A. Stubbs.
\newblock Predictor--corrector methods for a class of linear complementarity
  problems.
\newblock {\em SIAM Journal on Optimization}, 4:441--453, 1994.

\bibitem{ipm:Mehrotra14}
S.~Mehrotra and J.~Sun.
\newblock An algorithm for convex quadratic programming that requires
  ${O(n^{3.5}L)}$ arithmetic operations.
\newblock {\em Mathematics of Operations Research}, 15:342--363, 1990.

\bibitem{ipm:Mehrotra12}
S.~Mehrotra and J.~Sun.
\newblock An interior point algorithm for solving smooth convex programs based
  on {Newton's} method.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 265--284. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Mehrotra15}
S.~Mehrotra and J.~Sun.
\newblock Path--following methods for convex programming.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Department of Industrial Engineering and Management Science, Northwestern
  University, Evanston, IL~60208, USA, July 1990.

\bibitem{ipm:Mehrotra11}
S.~Mehrotra and J.~Sun.
\newblock A method of analytic centers for quadratically constrained convex
  quadratic programs.
\newblock {\em SIAM Journal on Numerical Analysis}, 28(2):529--544, 1991.

\bibitem{ipm:Mehrotra13}
S.~Mehrotra and J.~Sun.
\newblock On computing the center of a quadratically constrained set.
\newblock {\em Mathematical Programming}, 50:81--89, 1991.

\bibitem{ipm:Mehrotra10}
S.~Mehrotra and J.~Sun.
\newblock On the implementation of a (primal--dual) interior point method.
\newblock {\em SIAM Journal on Optimization}, 2(4):575--601, 1992.

\bibitem{ipm:Mehrotra30}
S.~Mehrotra and J.-S. Wang.
\newblock Conjugate gradient based implementation of interior point methods for
  network flow problems.
\newblock In L.~Adams and J.~L. Nazareth, editors, {\em Linear and Nonlinear
  Conjugate Gradient--Related Methods (Proceedings of the AMS--IMS--SIAM Joint
  Summer Research Conference, Seattle, WA, USA, July 9--13, 1995)}, pages
  124--142. SIAM Publications, Philadelphia, PA, USA, 1996.

\bibitem{ipm:Mehrotra21}
S.~Mehrotra and Y.~Ye.
\newblock On finding the optimal facet of linear programs.
\newblock {Technical Report} TR~91--10, Department of Industrial Engineering
  and Management Sciences, Northwestern University, Evanston, IL~60208, USA,
  1991.
\newblock See also Mehrotra and Ye\,\cite{ipm:Mehrotra28}.

\bibitem{ipm:Mehrotra28}
S.~Mehrotra and Y.~Ye.
\newblock Finding an interior point in the optimal face of linear programs.
\newblock {\em Mathematical Programming}, 62:497--515, 1993.
\newblock See also Mehrotra and Ye\,\cite{ipm:Mehrotra21}.

\bibitem{ipm:Meketon3}
M.~S. Meketon.
\newblock Least absolute value regression.
\newblock {Working Paper}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974,
  USA, 1985.

\bibitem{ipm:Meketon2}
M.~S. Meketon.
\newblock Optimization in simulation\,: {A} survey of recent results.
\newblock In A.~Thesen, H.~Grant, and W.~D. Kelton, editors, {\em Proceedings
  of the Winter Simulation Conference held in Atlanta, GA~30322, USA,December
  1987}, pages 58--67. ACM Press, New York, NY, USA, 1987.

\bibitem{ipm:Meketon1}
M.~S. Meketon and R.~J. Vanderbei.
\newblock Degeneracy issues in the affine scaling algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
  USA}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA, October 1987.

\bibitem{ipm:Mello1}
{J. C. O.} Mello, A.~C.~G. Melo, and S.~Granville.
\newblock Simultaneous transfer capability assessment by combining interior
  point methods and {Monte Carlo} simulation.
\newblock {\em IEEE Transaction on Power Systems}, 12:736--742, 1997.

\bibitem{ipm:Melman2}
A.~Melman.
\newblock A new linesearch method for quadratically constrained convex
  programming.
\newblock {\em Operations Research Letters}, 16:67--77, 1994.

\bibitem{ipm:Melman4}
A.~Melman.
\newblock A linesearch procedure in barrier methods for some convex programming
  problems.
\newblock {\em SIAM Journal on Optimization}, 6:283--298, 1996.

\bibitem{ipm:Melman1}
A.~Melman and R.~Polyak.
\newblock Newton modified barrier function complexity for quadratic programming
  problems.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, California Institute of Technology, USA, May 1992.

\bibitem{ipm:Melman3}
A.~Melman and R.~Polyak.
\newblock The {Newton} modified barrier method for {QP} problems.
\newblock {\em Annals of Operations Research}, 62:465--519, 1996.

\bibitem{ipm:Mendel1}
M.~Mendel.
\newblock {Primal--duale pfadorientierte Innere--{\"A}u{\ss}ere--Punkte--%
  Verfahren zur L{\"o}sung linearer Optimierungsaufgaben (Primal--dual
  path--following interior--exterior--point methods for solving linear
  programming problems)}.
\newblock {Habilitationthesis}, Fachbereich Mathematik, Bergische
  Universit{\"a}t-- Gesamthochschule Wuppertal, Gauss--str. 20,
  D--42097~Wuppertal, Germany, 1996.
\newblock (In German).

\bibitem{ipm:Mennicken1}
J.~Mennicken.
\newblock Implementation of a first order central path following algorithm for
  solving large linear programs.
\newblock {Technical Report} 202, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, 1990.

\bibitem{ipm:Merle1}
{O. du} Merle.
\newblock {\em Mise en oeuvre et developpements de la methode de plans coupants
  bases sur les centres analytique ({Interior} points and cutting planes\,:
  {Development} and implementation of methods for convex optimization and large
  scale structured linear programming)}.
\newblock PhD thesis, Department of Management Studies, University of Geneva,
  CH--1211 Geneva, Switzerland, 1995.
\newblock (In French).

\bibitem{ipm:Mesbahi1}
M.~Mesbahi and G.~P. Papavassilopoulos.
\newblock {LMIs}, interior point methods, complexity theory, and robust
  analysis.
\newblock {\em Proceedings of the 35th IEEE conference on Decision and
  Control}, 4/4:4625--4630, 1996.

\bibitem{ipm:Meszaros1}
C.~M{\'e}sz{\'a}ros.
\newblock On the modifications of the affine scaling algorithm for linear
  programming.
\newblock {\em Alkamazott Matematikai Lapok}, 17:185--194, 1993.
\newblock (In Hungarian, English summary).

\bibitem{ipm:Meszaros2}
C.~M{\'e}sz{\'a}ros.
\newblock The {''inexact''} minimum local fill--in ordering algorithm.
\newblock {Working Paper} WP 95--7, Computer and Automation Research Institute,
  Department of Operations Research and Decision Systems, Hungarian Academy of
  Sciences, H--1518~Budapest, Hungary, November 1995.
\newblock Submitted to {\em{ACM Transactions on Mathematical Software}}.

\bibitem{ipm:Meszaros7}
C.~M{\'e}sz{\'a}ros.
\newblock {\em The efficient implementation of interior point methods for
  linear programming and their applications}.
\newblock PhD thesis, E{\"o}tv{\"o}s Lor{\'a}nd University of Sciences,
  Budapest, Hungary, 1996.

\bibitem{ipm:Meszaros4}
C.~M{\'e}sz{\'a}ros.
\newblock Fast {Cholesky} factorization of interior point methods of linear
  programming.
\newblock {\em Computers and Mathematics with Applications}, 31:49--54, 1996.

\bibitem{ipm:Meszaros3}
C.~M{\'e}sz{\'a}ros.
\newblock The augmented system variant of {IPM}s in two--stage stochastic
  linear programming computation.
\newblock {\em European Journal of Operational Research}, 101:317--327, 1997.

\bibitem{ipm:Meszaros6}
C.~M{\'e}sz{\'a}ros.
\newblock Steplengths in infeasible primal--dual interior point algorithms for
  convex quadratic programming.
\newblock {Technical Report} DOC~97/7, Imperial College, London, United
  Kingdom, July 1997.

\bibitem{ipm:Meszaros9}
C.~M{\'e}sz{\'a}ros.
\newblock On aproperty of the {Cholesky} factorization and its consequences in
  interior point methods.
\newblock {Working Paper} WP\,98--7, Laboratory of Operations Research and
  Decision Systems, Hungarian Academy of Sciences, Budapest, Hungary, April
  1998.

\bibitem{ipm:Meszaros5}
C.~M{\'e}sz{\'a}ros.
\newblock On free variables in interior point methods.
\newblock {\em Optimization Methods and Software}, 9:121--139, 1998.

\bibitem{ipm:Meszaros10}
C.~M{\'e}sz{\'a}ros.
\newblock On the sparsity issues of interior point methods for quadratic
  programming.
\newblock {Working Paper} WP\,98--4, Laboratory of Operations Research and
  Decision Systems, Hungarian Academy of Sciences, Budapest, Hungary, 1998.

\bibitem{ipm:Meszaros8}
C.~M{\'e}sz{\'a}ros.
\newblock The separable and non--separable formulations of convex quadratic
  problems in interior point methods.
\newblock {Working Paper} WP\,98--3, Laboratory of Operations Research and
  Decision Systems, Hungarian Academy of Sciences, Budapest, Hungary, April
  1998.

\bibitem{ipm:Meyer1}
R.~R. Meyer and G.~L. Schultz.
\newblock Structured interior point methods for multicommodity flows.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Department of Computer Science, University of Wisconsin, Madison,
  WI~53706, USA, October 1990.

\bibitem{ipm:Miagen1}
S.~Miagen and T.~Miyazaki.
\newblock Implementation and numerical experiments on an interior--point
  algorithm for linear programming.
\newblock In {\em Proceedings of the InfoJapan~'90\ : Information Technology
  Harmonizing with Society, Tokyo, Japan, Oct.\ 1990}, volume~1, pages 19--25.
  North Holland, Amsterdam, The Netherlands, 1990.

\bibitem{ipm:Miao2}
J.~Miao.
\newblock A quadratically convergent {$O((1 + \kappa)\sqrt{n}L)$}-- iteration
  algorithm for the {$P_{*}(\kappa)$}--matrix linear complementarity problem.
\newblock {Research Report} RRR~93--93, RUTCOR\,--\,Rutgers Center for
  Operations Research, Rutgers University, Busch Campus, New Brunswick,
  NJ~08903, USA, 1993.

\bibitem{ipm:Miao1}
J.~Miao.
\newblock Two infeasible interior--point predictor--corrector algorithms for
  linear programming.
\newblock {\em SIAM Journal on OPtimization}, 6:587--599, 1996.

\bibitem{ipm:Minoux1}
M.~Minoux.
\newblock New suggested implementation of {Karmarkar's} algorithm.
\newblock Cahier~71, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, May 1986.

\bibitem{ipm:Minoux3}
M.~Minoux.
\newblock Towards a probabilistic analysis of {Karmarkar's} algorithm.
\newblock Cahier, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1990.

\bibitem{ipm:Minoux2}
M.~Minoux.
\newblock Probabilistic bounds on one step objective/potential function
  improvement in {Karmarkar's} algorithm.
\newblock {\em R.A.I.R.O Recherche Operationnelle/Operations Research},
  28:329--355, 1994.

\bibitem{ipm:Mitchell1}
J.~E. Mitchell.
\newblock {\em Karmarkar's algorithm and combinatorial optimization problems}.
\newblock PhD thesis, School of Operations Research and Industrial Engineering,
  Cornell University, Ithaca, NY~14853--7501, USA, 1988.

\bibitem{ipm:Mitchell13}
J.~E. Mitchell.
\newblock An interior point column generation method for linear programming
  using shifted barriers.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Rensselaer Polytechnic Institute, Department of Mathematical Sciences,
  Troy, NY~12180--3590, USA, November 1991.

\bibitem{ipm:Mitchell11}
J.~E. Mitchell.
\newblock Updating lower bounds when using {Karmarkar's} projective algorithm
  for linear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 78:127--142,
  1993.

\bibitem{ipm:Mitchell8}
J.~E. Mitchell.
\newblock An interior point column generation method for linear programming
  using shifted barriers.
\newblock {\em SIAM Journal on Optimization}, 4:423--440, 1994.

\bibitem{ipm:Mitchell19}
J.~E. Mitchell.
\newblock Interior point methods for combinatorial optimization.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 417--466. Kluwer
  Academic Publishers, Dordrecht, The Netherlands, 1996.
\newblock See also Mitchell, Pardalos and Resende\,\cite{ipm:Mitchell23}.

\bibitem{ipm:Mitchell16}
J.~E. Mitchell.
\newblock Interior point methods for integer programming.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
  Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
  Applications}, pages 223--248. Oxford Science Publications, Oxford University
  Press, Oxford, Great Britain, 1996.

\bibitem{ipm:Mitchell20}
J.~E. Mitchell.
\newblock Computational experience with an interior point cutting plane
  algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, February 1997.
\newblock Revised April 1997.

\bibitem{ipm:Mitchell18}
J.~E. Mitchell.
\newblock Fixing variables and generating classical cutting planes when using
  an interior branch and cut method to solve integer programming problems.
\newblock {\em European Journal of Operational Research}, 97:139--148, 1997.

\bibitem{ipm:Mitchell21}
J.~E. Mitchell.
\newblock An interior point cutting plane algorithm for {Ising}spin glass
  problems.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, July 1997.
\newblock Revised April 1997.

\bibitem{ipm:Mitchell14}
J.~E. Mitchell and B.~Borchers.
\newblock A primal--dual interior point cutting plane method for the linear
  ordering problem.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Bulletin}, 21:13--18, 1992.

\bibitem{ipm:Mitchell15}
J.~E. Mitchell and B.~Borchers.
\newblock Solving real--world linear ordering problems using a primal--dual
  interior point cutting plane method.
\newblock {\em Annals of Operatiomns Research}, 62:253--276, 1996.

\bibitem{ipm:Mitchell22}
J.~E. Mitchell and B.~Borchers.
\newblock Solving linear ordering problems with a combined interior
  point/simplex cutting plane algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, September 1997.

\bibitem{ipm:Mitchell23}
J.~E. Mitchell, P.~M. Pardalos, and M.~G.~C. Resende.
\newblock Interior point methods for combinatorial optimization.
\newblock In D.-Z. Du and P.~M. Pardalos, editors, {\em Handbook of
  Combinatorial Optimization}, pages 189--298. Kluwer Academic Publishers,
  Dordrecht, The Netherlands, 1998.
\newblock See also Mitchell\,\cite{ipm:Mitchell19}.

\bibitem{ipm:Mitchell17}
J.~E. Mitchell and S.~Ramaswamy.
\newblock A long--step, cutting plane algorithm for linear and convex
  programming.
\newblock {Technical Report} 37--93--387, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, August 1993.
\newblock Title before August 1994 revision\,: {An extension of Atkinson and
  Vaidya's algorithm that uses central trajectory}.

\bibitem{ipm:Mitchell12}
J.~E. Mitchell and M.~J. Todd.
\newblock Two variants of {Karmarkar's} linear programming algorithm for
  problems with some unrestricted variables.
\newblock {Technical Report} 741, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--7501, USA, 1987.
\newblock Incorporated in Mitchell and Todd \cite{ipm:Mitchell4}.

\bibitem{ipm:Mitchell3}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving linear ordering problems using {Karmarkar's} algorithm.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--7501, USA, 1988.
\newblock Incorrect citation, elsewhere; part of Mitchell \cite{ipm:Mitchell1},
  and of Mitchell and Todd \cite{ipm:Mitchell6}.

\bibitem{ipm:Mitchell2}
J.~E. Mitchell and M.~J. Todd.
\newblock On the relationship between the search directions in the affine and
  projective variants of {Karmarkar's} linear programming algorithm.
\newblock In B.~Cornet and H.~Tulkens, editors, {\em Contributions to
  Operations Research and Economics\,: The Twentieth Anniversary of CORE},
  pages 237--250. M.I.T. Press, Cambridge, MA, USA, 1989.

\bibitem{ipm:Mitchell5}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
  algorithm, {Part\,I\,: Theory}.
\newblock {RPI Technical Report} 172, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, January 1989.

\bibitem{ipm:Mitchell6}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
  algorithm, {Part\,II\,: Computational} results.
\newblock {RPI Technical Report} 173, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, January 1989.

\bibitem{ipm:Mitchell7}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving perfect matching problems using {Karmarkar's} algorithm.
\newblock {RPI Technical Report} 174, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, August 1989.
\newblock See Mitchell and Todd \cite{ipm:Mitchell10}, too.

\bibitem{ipm:Mitchell4}
J.~E. Mitchell and M.~J. Todd.
\newblock A variant of {Karmarkar's} linear programming algorithm for problems
  with some unrestricted variables.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 10:30--38,
  1989.

\bibitem{ipm:Mitchell10}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving perfect matching problems using {Karmarkar's} algorithm.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 309--318. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Mitchell9}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
  algorithm.
\newblock {\em Mathematical Programming}, 56:245--284, 1992.
\newblock Combination and shortening of Mitchell and Todd
  \cite{ipm:Mitchell5,ipm:Mitchell6}.

\bibitem{ipm:Mitra3}
G.~Mitra and R.~Levkovitz.
\newblock {\em {Interior Point Methods for Linear Programming Optimization\,:
  Theory and Practice}}.
\newblock John Wiley\,\&\,Sons, New York, USA, 1997.

\bibitem{ipm:Mitra2}
G.~Mitra, M.~Tamiz, and J.~Yadegar.
\newblock Experimental investigation of an interior search method within a
  simplex framework.
\newblock {\em Communications of the ACM}, 31(12):1474--1482, 1988.

\bibitem{ipm:Mitra1}
G.~Mitra, M.~Tamiz, and J.~Yadegar.
\newblock A hybrid algorithm for linear programming.
\newblock In A.~J. Osiadacz, editor, {\em Simulation and Optimization of Large
  Systems}, volume~13 of {\em The Institute of Mathematics and Its Applications
  Conference Series}, pages 143--159. Clarendon Press, Oxford, England, 1988.

\bibitem{ipm:Mizuno1}
S.~Mizuno.
\newblock An ${O(n^{3}L)}$ algorithm using a sequence for linear
  complementarity problems.
\newblock {\em Journal of the Operations Research Society of Japan}, 33:66--75,
  1990.

\bibitem{ipm:Mizuno2}
S.~Mizuno.
\newblock A rank--one updating interior algorithm for linear programming.
\newblock {\em Arabian Journal for Science and Engineering}, 15(4):671--677,
  1990.

\bibitem{ipm:Mizuno10}
S.~Mizuno.
\newblock {$O(n^{\rho}L)$} iteration {$O(n^{3}L)$} potential reduction
  algorithms for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:155--168, 1991.

\bibitem{ipm:Mizuno9}
S.~Mizuno.
\newblock A new polynomial time method for a linear complementarity problem.
\newblock {\em Mathematical Programming}, 56:31--43, 1992.

\bibitem{ipm:Mizuno16}
S.~Mizuno.
\newblock Polynomiality of the {Kojima--Megiddo--Mizuno} infeasible interior
  point algorithm for linear programming.
\newblock {Technical Report} 1006, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, May 1992.
\newblock See also Mizuno \cite{ipm:Mizuno21}.

\bibitem{ipm:Mizuno17}
S.~Mizuno.
\newblock A primal--dual interior point method for linear programming.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--252, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, January 1992.
\newblock (In Japanese).

\bibitem{ipm:Mizuno21}
S.~Mizuno.
\newblock Polynomiality of infeasible interior--point algorithms for linear
  programming.
\newblock {\em Mathematical Programming}, 67:109--119, 1994.
\newblock See also Mizuno \cite{ipm:Mizuno16}.

\bibitem{ipm:Mizuno22}
S.~Mizuno.
\newblock A predictor--corrector infeasible--interior--point algorithm for
  linear programming.
\newblock {\em Operations Research Letters}, 16:61--66, 1994.

\bibitem{ipm:Mizuno24}
S.~Mizuno.
\newblock Research in interior--point methods.
\newblock {\em Proceedings of the Institute of Statistical Mathematics (Tokyo,
  Japan)}, 42:103--109, 1994.
\newblock (In Japanese).

\bibitem{ipm:Mizuno27}
S.~Mizuno.
\newblock Infeasible--interior--point algorithms.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 159--187. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Mizuno25}
S.~Mizuno.
\newblock A superlinearly convergent infeasible--interior--point algorithm for
  geometrical {LCPs} without a strictly complementarity condition.
\newblock {\em Mathematics of Operations Research}, 21:382--400, 1996.

\bibitem{ipm:Mizuno23}
S.~Mizuno and F.~Jarre.
\newblock An infeasible--interior--point algorithm using projections onto a
  convex set.
\newblock {\em Annals of Operations Research}, 62:59--80, 1993.
\newblock See also Mizuno and Jarre \cite{ipm:Jarre18}.

\bibitem{ipm:Mizuno29}
S.~Mizuno and F.~Jarre.
\newblock Global and polynomial--time convergence of an
  infeasible--interior--point algorithm using inexact computation.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 981:22--35,
  1997.
\newblock See also Mizuno and Jarre\,\cite{ipm:Mizuno31}.

\bibitem{ipm:Mizuno31}
S.~Mizuno and F.~Jarre.
\newblock Global and polynomial--time convergence of an
  infeasible--interior--point algorithm using inexact computation.
\newblock {\em Mathematical Programming}, 84:39--53, 1999.
\newblock See also Mizuno and Jarre\,\cite{ipm:Mizuno29}.

\bibitem{ipm:Mizuno26}
S.~Mizuno, F.~Jarre, and J.~Stoer.
\newblock A unified approach to infeasible--interior--point algorithms via
  geometrical linear complementarity problems.
\newblock {\em Applied Mathematics\,\&\,Optimization}, 33:315--341, 1996.

\bibitem{ipm:Mizuno19}
S.~Mizuno, M.~Kojima, and M.~J. Todd.
\newblock Infeasible--interior--point primal--dual potential--reduction
  algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:52--67, 1995.

\bibitem{ipm:Mizuno3}
S.~Mizuno and K.~Masuzawa.
\newblock Polynomial time interior point algorithms for transportation
  problems.
\newblock {\em Journal of the Operations Research Society of Japan},
  32:371--382, 1989.

\bibitem{ipm:Mizuno28}
S.~Mizuno, N.~Megiddo, and T.~Tsuchiya.
\newblock A linear programming instance with many crossover events.
\newblock {\em Journal of Complexity}, 12:474--479, 1996.

\bibitem{ipm:Mizuno14}
S.~Mizuno and A.~Nagasawa.
\newblock Strict monotonicity in {Todd's} low--complexity algorithm for linear
  programming.
\newblock {\em Operations Research Letters}, 12:59--64, 1992.

\bibitem{ipm:Mizuno15}
S.~Mizuno and A.~Nagasawa.
\newblock A primal--dual affine scaling potential reduction algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 62:119--131, 1993.

\bibitem{ipm:Mizuno13}
S.~Mizuno, R.~Saigal, and J.~B. Orlin.
\newblock Determination of optimal vertices from feasible solution in
  unimodular programming.
\newblock {\em Mathematical Programming}, 59:23--31, 1993.

\bibitem{ipm:Mizuno11}
S.~Mizuno and M.~J. Todd.
\newblock An {$O(n^{3}L)$} long step path following algorithm for a linear
  complementarity problem.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1989.
\newblock Same as Mizuno and Todd \cite{ipm:Mizuno12}.

\bibitem{ipm:Mizuno12}
S.~Mizuno and M.~J. Todd.
\newblock An {$O(n^{3}L)$} adaptive path following algorithm for a linear
  complementarity problem.
\newblock {\em Mathematical Programming}, 52:587--595, 1991.

\bibitem{ipm:Mizuno30}
S.~Mizuno and M.~J. Todd.
\newblock On two homogeneous self--dual systems for linear programming and its
  extensions.
\newblock {Research Memorandum} 687, The Institute of Statistical Mathematics,
  4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, 1998.
\newblock Also issued as {Technical Report No.\,1213, School of Operations
  Research and Industrial Engineering, Cornell University, Ithaca,
  NY~14853--3801, USA}.

\bibitem{ipm:Mizuno18}
S.~Mizuno, M.~J. Todd, and L.~Tun{\c c}el.
\newblock Monotonicity of primal and dual objective values in primal--dual
  interior--point algorithms.
\newblock {\em SIAM Journal on Optimization}, 4:613--625, 1994.

\bibitem{ipm:Mizuno4}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of path--following algorithms for linear
  programming.
\newblock {Technical Report} 878, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1989.
\newblock See Mizuno et al.\ \cite{ipm:Mizuno8}.

\bibitem{ipm:Mizuno6}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of interior point algorithms for linear
  programming.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1990.
\newblock Incorrect citation, elsewhere.

\bibitem{ipm:Mizuno5}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of long--step algorithms for linear programming.
\newblock {Technical Report} 882, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1990.
\newblock Also available as {\em Technical Report 24, Department of Management
  Science and Engineering, Tokyo Institute of Technology, Oh--Okayama,
  Meguro--ku, Tokyo~152, Japan, 1989} and {\em Technical Report 89--23,
  Department of Management Science, University of Iowa, Iowa City, IA~52242,
  USA, 1989}. See also Mizuno et al.\, \cite{ipm:Mizuno8}.

\bibitem{ipm:Mizuno8}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock On adaptive--step primal--dual interior--point algorithms for linear
  programming.
\newblock {\em Mathematics of Operations Research}, 18:964--981, 1993.
\newblock Revised and combined version of Mizuno et al.\,
  \cite{ipm:Mizuno4,ipm:Mizuno5}.

\bibitem{ipm:Mizuno20}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock A surface of analytic centers and infeasible--interior--point
  algorithms for linear programming.
\newblock {\em Mathematics of Operations Research}, 20:135--162, 1995.

\bibitem{ipm:Mizuno7}
S.~Mizuno, A.~Yoshise, and T.~Kikuchi.
\newblock Practical polynomial time algorithms for linear complementarity
  problems.
\newblock {\em Journal of the Operations Research Society of Japan}, 32:75--92,
  1989.

\bibitem{ipm:Momoh7}
J.~A. Momoh, R.~F. Austin, R.~Adapa, and E.~C. Ogbuobiri.
\newblock Application of interior point method to economic dispatch.
\newblock {\em Proceedings of the IEEE International Conference on Systems, Man
  and Cybernetics (Chicago, IL, USA, October 1992)}, 2:1096--1101, 1993.

\bibitem{ipm:Momoh4}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock Evaluation of interior point methods and their application to power
  systems economic dispatch.
\newblock {\em Proceedings of the 1993 North American Power Symposium
  (Washington, D.C., USA, October 1993)}, pages 116--123, 1994.

\bibitem{ipm:Momoh2}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock Rule based support for partioning networks for optimal power flows.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
  Symposium (Manhattan, KS, USA, September 1994)}, 1:376--381, 1994.

\bibitem{ipm:Momoh5}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock {VAr} planning using partitioned power system networks.
\newblock {\em Proceedings of the 36th Midwest Symposium on Circuits and
  Systems (Detroit, MI, USA, August 1993)}, 1:372--376, 1994.

\bibitem{ipm:Momoh3}
J.~A. Momoh and S.~X. Guo.
\newblock An enhanced quadratic interior point method to solve power system
  {VAr} planning.
\newblock {\em Proceedings of the 1993 North American Power Symposium
  (Washington, D.C., USA, October 1993)}, pages 215--221, 1994.

\bibitem{ipm:Momoh1}
J.~A. Momoh, S.~X. Guo, E.~C. Ogbuobiri, and R.~Adapa.
\newblock The quadratic interior point method solving power system optimization
  problems.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:1327--1336, 1994.
\newblock See also\,: {\em IEEE International Conference on Systems, Man and
  Cybernetics 1\,(1992), 1096--}.

\bibitem{ipm:Momoh6}
J.~A. Momoh, P.~J. Lusaka, R.~Adapa, and E.~C. Ogbuobiri.
\newblock Heurstic--based algorithms for enhanced interior point based {OPF}.
\newblock {\em Expert System Application to Power Systems (Proceedings of the
  January 1993 Melbourne Conference)}, IV:686--696, 1994.

\bibitem{ipm:Monma1}
C.~L. Monma.
\newblock Recent breakthroughs in linear programming methods.
\newblock {Internal Memorandum}, Bell Communications Research, Morristown,
  NJ~07960, USA, 1987.

\bibitem{ipm:Monma2}
C.~L. Monma.
\newblock Successful implementations of interior algorithms.
\newblock {\em SIAM News}, 22(2):14--16, March 1989.

\bibitem{ipm:Monma3}
C.~L. Monma and A.~J. Morton.
\newblock Computational experience with the dual affine variant of
  {Karmarkar's} method for linear programming.
\newblock {\em Operations Research Letters}, 6:261--267, 1987.

\bibitem{ipm:Monteiro9}
R.~D.~C. Monteiro.
\newblock Convergence and boundary behavior of the projective scaling
  trajectories for linear programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 213--229. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Monteiro10}
R.~D.~C. Monteiro.
\newblock Convergence and boundary behavior of the projective scaling
  trajectories for linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):842--858, 1991.

\bibitem{ipm:Monteiro13}
R.~D.~C. Monteiro.
\newblock The global convergence of a class of primal potential reduction
  algorithms for convex programming.
\newblock {Technical Report}, Department of Systems and Industrial Engineering,
  University of Arizona, Tucson, AZ~85721, USA, August 1991.

\bibitem{ipm:Monteiro8}
R.~D.~C. Monteiro.
\newblock An implementation of range analysis for {LP} problems solved via
  interior point methods.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Systems and Industrial Engineering,
  University of Arizona, Tucson, AZ~85721, USA, July 1991.

\bibitem{ipm:Monteiro1}
R.~D.~C. Monteiro.
\newblock On the continuous trajectories for a potential reduction algorithm
  for linear programming.
\newblock {\em Mathematics of Operations Research}, 17:225--253, 1992.

\bibitem{ipm:Monteiro11}
R.~D.~C. Monteiro.
\newblock A globally convergent primal--dual interior point algorithm for
  convex programming.
\newblock {\em Mathematical Programmingh}, 64:123--147, 1994.

\bibitem{ipm:Monteiro24}
R.~D.~C. Monteiro.
\newblock Primal--dual algorithms for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 7:663--678, 1997.
\newblock Former technical report title (Oct. 1995)\,: Primal--dual
  path--following algorithms for semidefinite programming.

\bibitem{ipm:Monteiro32}
R.~D.~C. Monteiro.
\newblock Polynomial convergence of primal--dual algorithms for semidefinite
  programming based on {Monteiro and Zhang} family of directions.
\newblock {\em SIAM Journal on Optimization}, 8:797--812, 1998.

\bibitem{ipm:Monteiro2}
R.~D.~C. Monteiro and I.~Adler.
\newblock An ${O(n^{3}L)}$ primal--dual interior point algorithm for linear
  programming.
\newblock {Technical Report} ORC~87--4, Department of Industrial Engineering
  and Operations Research, University of California, Berkeley, CA~94720, USA,
  1987.

\bibitem{ipm:Monteiro6}
R.~D.~C. Monteiro and I.~Adler.
\newblock A polynomial primal--dual affine algorithm for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, Engineering Systems Research Center, University of California,
  Berkeley, CA~94720, USA, October 1988.

\bibitem{ipm:Monteiro3}
R.~D.~C. Monteiro and I.~Adler.
\newblock Interior path following primal--dual algorithms\,: {Part\,I\,:
  Linear} programming.
\newblock {\em Mathematical Programming}, 44:27--41, 1989.

\bibitem{ipm:Monteiro4}
R.~D.~C. Monteiro and I.~Adler.
\newblock Interior path following primal--dual algorithms\,: {Part\,II\,:
  Convex} quadratic programming.
\newblock {\em Mathematical Programming}, 44:43--66, 1989.

\bibitem{ipm:Monteiro5}
R.~D.~C. Monteiro and I.~Adler.
\newblock An extension of {Karmarkar--type} algorithm to a class of convex
  separable programming problems with global linear rate of convergence.
\newblock {\em Mathematics of Operations Research}, 15:408--422, 1990.

\bibitem{ipm:Monteiro7}
R.~D.~C. Monteiro, I.~Adler, and M.~G.~C. Resende.
\newblock A polynomial--time primal--dual affine scaling algorithm for linear
  and convex quadratic programming and its power series extension.
\newblock {\em Mathematics of Operations Research}, 15:191--214, 1990.

\bibitem{ipm:Monteiro25}
R.~D.~C. Monteiro and S.~Mehrotra.
\newblock A general parametric analysis approach and its implication to
  sensitivity analysis in interior point methods.
\newblock {\em Mathematical Programming}, 72:65--82, 1996.

\bibitem{ipm:Monteiro26}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock Properties of an interior--point mapping for mixed complementarity
  problems.
\newblock {\em Mathematics of Operations Research}, 21:629--654, 1996.

\bibitem{ipm:Monteiro29}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock A potential reduction {Newton} method for constrained equations.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30322--0205, USA, March 1997.

\bibitem{ipm:Monteiro35}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock On two interior--point mappings for nonlinear semidefinite
  complementarity problems.
\newblock {\em Mathematics of Operations Research}, 23:39--60, 1998.

\bibitem{ipm:Monteiro15}
R.~D.~C. Monteiro, J.-S. Pang, and T.~Wang.
\newblock A positive algorithm for the nonlinear complementarity problem.
\newblock {\em SIAM Journal on Optimization}, 5:129--148, 1995.

\bibitem{ipm:Monteiro14}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Limiting behavior of the derivatives of certain trajectories
  associated with a monotone horizontal linear complementarity problem.
\newblock {\em Mathematics of Operations Research}, 21:793--814, 1996.

\bibitem{ipm:Monteiro30}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomial convergence of a new family of primal--dual algorithms for
  semidefinite programming.
\newblock {Research Memorandum} 627, The Institute of Statistical Mathematics,
  4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, 1996.

\bibitem{ipm:Monteiro31}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomiality of primal--dual algorithms for semidefinite linear
  complementarity problems based on the {Kojima--Shindoh--Hara} family of
  directions.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
  1004:138--152, 1997.
\newblock See also Monteiro and Tsuchiya\,\cite{ipm:Monteiro38}.

\bibitem{ipm:Monteiro21}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Global convergence of the affine scaling method for convex quadratic
  programming.
\newblock {\em SIAM Journal on Optimization}, 8:26--58, 1998.

\bibitem{ipm:Monteiro37}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomial convergence of primal--dual algorithms for the
  second--order cone program based on the {MZ}--family of directions.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30338, USA, May 1998.

\bibitem{ipm:Monteiro38}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomiality of primal--dual algorithms for semidefinite linear
  complementarity problems based on the {Kojima--Shindoh--Hara} family of
  directions.
\newblock {\em Mathematical Programming}, 84:39--53, 1999.
\newblock See also Monteiro and Tsuchiya\,\cite{ipm:Monteiro31}.

\bibitem{ipm:Monteiro19}
R.~D.~C. Monteiro, T.~Tsuchiya, and Y.~Wang.
\newblock A simplified global convergence proof of the affine scaling
  algorithm.
\newblock {\em Annals of Operations Research}, 46/47:443--482, 1993.

\bibitem{ipm:Monteiro23}
R.~D.~C. Monteiro and Y.~Wang.
\newblock Trust region affine scaling algorithms for linearly constrained
  convex and concave programs.
\newblock {\em Mathematical Programming}, 80:283--313, 1998.

\bibitem{ipm:Monteiro12}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock A globally and superlinearly convergent potential reduction interior
  point method for convex programming.
\newblock {Technical Report} 92--13, Department of Systems and Industrial
  Engineering, University of Arizona, Tucson, AZ~85721, USA, July 1992.
\newblock Also available as {\em Technical Report MSC--P316--0792, Mathematical
  and Computer Science Division, Argonne National Laboratory, Argonne,
  IL~60439, USA, July 1992}.

\bibitem{ipm:Monteiro20}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock Interior--point algorithms for degenerate linear complementarity
  problems.
\newblock {\em Computational Optimization and Applications}, 3:131--155, 1994.

\bibitem{ipm:Monteiro16}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock Local convergence of interior--point algorithms for degenerate
  monotone {LCP}.
\newblock {\em Computational Optimization and Applications}, 3:131--155, 1994.

\bibitem{ipm:Monteiro17}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock Superlinear primal--dual affine scaling algorithms for {LCP}.
\newblock {\em Mathematical Programming}, 69:311--333, 1995.

\bibitem{ipm:Monteiro18}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock A superlinear infeasible--interior--point affine scaling algorithm
  for {LCP}.
\newblock {\em SIAM Journal on Optimization}, 6:1--18, 1996.

\bibitem{ipm:Monteiro28}
R.~D.~C. Monteiro and P.~R. Zanj{\'a}como.
\newblock Implementation of primal--dual methods for semidefinite programming
  based on {Monteiro} and {Tsuchiya} {Newton} directions and their variants.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30322--0205, USA, July 1997.

\bibitem{ipm:Monteiro33}
R.~D.~C. Monteiro and P.~R. Zanj{\'a}como.
\newblock A note on the existence of the {Alizadeh--Haeberly--Overton}
  direction for semidefinite programming.
\newblock {\em Mathematical Programming}, 78:393--396, 1997.

\bibitem{ipm:Monteiro36}
R.~D.~C. Monteiro and P.~R. Zanj{\'a}como.
\newblock General interior--point maps and existence of weighted paths for
  nonlinear semidefinite complementarity problems.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30322--0205, USA, April 1998.

\bibitem{ipm:Monteiro34}
R.~D.~C. Monteiro and Y.~Zhang.
\newblock A unified analysis for a class of path--following primal--dual
  interior--point algorithms for semidefinite programming.
\newblock {\em Mathematical Programming}, 81:281--299, 1998.

\bibitem{ipm:Monteiro22}
R.~D.~C. Monteiro and F.~Zhou.
\newblock On superlinear convergence of infeasible--interior--point algorithms
  for linearly constrained convex programs.
\newblock {\em Computational Optimization and Applications}, 8:245--262, 1998.

\bibitem{ipm:Monteiro27}
R.~D.~C. Monteiro and F.~Zhou.
\newblock On the existence and convergence of the central path for convex
  programming and some duality results.
\newblock {\em Computational Optimization and Applications}, 10:51--77, 1998.

\bibitem{ipm:Morales1}
J.~L. {Morales--P{\'e}rez} and R.~W.~H. Sargent.
\newblock Numerical experiments with an interior point method for large scale
  convex quadratic programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Centre for Process Systems Engineering, Imperial College, London,
  United Kingdom, May 1992.
\newblock See also Morales--P{\'e}rez and Sargent \cite{ipm:Morales2}.

\bibitem{ipm:Morales2}
J.~L. {Morales--P{\'e}rez} and R.~W.~H. Sargent.
\newblock On the implementation and performance of an interior point method for
  large sparse convex quadratic programming.
\newblock {\em Optimization Methods and Software}, 1:153--168, 1992.

\bibitem{ipm:More1}
J.~J. Mor{\'e} and S.~J. Wright.
\newblock {\em {Optimization Software Guide}}, volume~14 of {\em Frontiers in
  Applied Mathematics}.
\newblock SIAM Publications, Philadelphia, PA~19101, USA, November 1993.

\bibitem{ipm:Morin1}
T.~L. Morin, B.~Haas, and T.~B. Trafalis.
\newblock Implementation of an interior point algorithm for multiobjective
  optimization.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Mathematics and Computer Science, School of Industrial
  Engineering, Purdue University, West Lafayette, IN~47907, USA, May 1990.

\bibitem{ipm:Morin3}
T.~L. Morin, N.~Prabhu, and Z.~Zhang.
\newblock Feasible gradients in the gravitational method for linear
  programming.
\newblock {\em Journal of the Operational Research Society of India
  (Opsearch)}, 32:253--265, 1995.

\bibitem{ipm:Morin4}
T.~L. Morin, N.~Prabhu, and Z.~Zhang.
\newblock Complexity of the gravitational method for linear programming.
\newblock In {\em Foundations of Software Technology and Theoretical Computer
  Science}, volume 1180 of {\em Lecture Notes in Computer Science}, pages
  212--223. Springer Verlag, Berlin, Germany, 1996.

\bibitem{ipm:Morin2}
T.~L. Morin and T.~B. Trafalis.
\newblock A polynomial--time algorithm for finding an efficient face of a
  polyhedron.
\newblock {Technical Report}, Department of Mathematics and Computer Science,
  School of Industrial Engineering, Purdue University, West Lafayette,
  IN~47907, USA, 1989.

\bibitem{ipm:Morshedi1}
A.~M. Morshedi and R.~A. Tapia.
\newblock Karmarkar as a classical method.
\newblock {Technical Report} TR~87--7, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, August 1987.

\bibitem{ipm:Mosheyev1}
L.~Mosheyev and M.~Zibulewsky.
\newblock Penalty/barriers multiplier algorithm for semidefinite programming\,:
  {Dual} bounds and inplementation.
\newblock {Research Report} 1/96, Optimization Laboratory, Faculty of
  Industrial Engineering and Management, Technion, Israel Institute of
  Technology, Haifa, Israel, 1996.

\bibitem{ipm:Mulkay1}
E.~L. Mulkay and S.~S. Rao.
\newblock Sequential linear programming with interior--point methods for
  large--scale optimization.
\newblock {\em Proceedings of the 1998 39th {AIAA/ASME/ASCE/AHS/ASC}
  Structures, Structural Dynamics, and Materials Conference and Exhibit and
  {AIAA/ASME/AHS} Adaptive Forum}, Part\,3/4:2175--2180, 1998.

\bibitem{ipm:Mueller1}
H.~M{\"u}ller-Merbach.
\newblock Right through the interior with the simplex technique.
\newblock {Technical Report}, University of Kaiserslautern,
  D--6100~Kaiserslautern, Germany, 1987.

\bibitem{ipm:Mulvey1}
J.~M. Mulvey and A.~Ruszczynski.
\newblock A diagonal quadratic approximation method for large scale linear
  programs.
\newblock {Technical Report} SOR~90--08, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1990.

\bibitem{ipm:Mulvey2}
J.~M. Mulvey and A.~Ruszczynski.
\newblock A parallel interior point method for multistage stochastic
  optimization.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, School of Engineering and Applied Science, Department of Civil
  Engineering and Operations Research, Princeton University, Princeton,
  NJ~08544, USA, November 1991.

\bibitem{ipm:Murai1}
M.~Murai.
\newblock An affine scaling algorithm for linear programming problem and its
  application to utility plant optimization.
\newblock {\em Transactions of the Institute of Systems, Control, and
  Information Engineers}, 10:62--69, 1997.

\bibitem{ipm:Muramatsu5}
M.~Muramatsu.
\newblock Affine scaling algorithm fails for semidefinite programming.
\newblock {\em Mathematical Programming}, 83:393--406, 1998.
\newblock See also {\it{S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku 1004
  (1997), 128--132}}.

\bibitem{ipm:Muramatsu1}
M.~Muramatsu and T.~Tsuchiya.
\newblock A convergence analysis of a long--step variant of the projective
  scaling algorithm.
\newblock {Research Memorandum} 454, The Institute of Statistical Mathematics,
  4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, November 1992.

\bibitem{ipm:Muramatsu3}
M.~Muramatsu and T.~Tsuchiya.
\newblock An affine scaling method with an infeasible starting point\,:
  {Convergence} analysis under nondegeneracy assumption.
\newblock {\em Annals of Operations Research}, 62:325--355, 1996.

\bibitem{ipm:Muramatsu2}
M.~Muramatsu and T.~Tsuchiya.
\newblock Convergence analysis of the projective scaling algorithm based on a
  long--step homogeneous affine scaling algorithm.
\newblock {\em Mathematical Programming}, 72:291--305, 1996.

\bibitem{ipm:Muramatsu4}
M.~Muramatsu and R.~J. Vanderbei.
\newblock Primal--dual affine--scaling algorithms fail for semidefinite
  programming.
\newblock {Technical Report} SOR~97--05, Department of Civil Engineering and
  Operations Research, Princeton University, Princeton, NJ~08544, USA, April
  1997.
\newblock Revised June 1997.

\bibitem{ipm:Murray2}
S.~M. Murray.
\newblock An interior point conjugate gradient approach to the generalized flow
  problem with costs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Operations Research, Stanford University, Stanford,
  CA~94305, USA, November 1991.

\bibitem{ipm:Murray4}
S.~M. Murray.
\newblock {\em An interior point approach to the generalized flow problem with
  costs and related problems}.
\newblock PhD thesis, Department of Operations Research, Stanford University,
  Stanford, CA~94305, USA, August 1992.

\bibitem{ipm:Murray1}
W.~Murray.
\newblock Methods for large--scale linear programming.
\newblock In S.~W. Wallace, editor, {\em Algorithms and Model Formulations in
  Mathematical Programming}, volume~51 of {\em NATO ASI Series F}, pages
  115--137. Springer Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Murray3}
W.~Murray and M.~H. Wright.
\newblock Line search procedures for the logarithmic barrier function.
\newblock {\em SIAM Journal on Optimization}, 4:229--246, 1994.

\bibitem{ipm:Murty2}
K.~G. Murty.
\newblock A new interior variant of the gradient projection method for linear
  programming.
\newblock {Technical Report} 85--18, Department of Operations Research,
  University of Michigan, Ann Arbor, MI~48103, USA, 1985.
\newblock See Murty \cite{ipm:Murty3}.

\bibitem{ipm:Murty3}
K.~G. Murty.
\newblock The gravitational method for linear programming.
\newblock {\em Journal of the Operational Research Society of India
  (Opsearch)}, 23:206--214, 1986.

\bibitem{ipm:Murty4}
K.~G. Murty.
\newblock {\em {Linear Complementarity, Linear and Nonlinear Programming}},
  volume~3 of {\em Sigma Series in Applied Mathematics}, chapter 11.4.1\,: {The
  Karmarkar's algorithm for linear programming}, pages 469--494.
\newblock Heldermann Verlag, Nassauische~Str.~26, D--1000~Berlin~31, Germany,
  1988.

\bibitem{ipm:Murty5}
K.~G. Murty.
\newblock {\em {Linear Complementarity, Linear and Nonlinear Programming}},
  volume~3 of {\em Sigma Series in Applied Mathematics}, chapter 11.4.4\,: {The
  gravitational method for linear programming}, pages 498--506.
\newblock Heldermann Verlag, Nassauische~Str.~26, D--1000~Berlin~31, Germany,
  1988.

\bibitem{ipm:Murty1}
K.~G. Murty and Y.~Fathi.
\newblock A feasible direction method for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Boston, MA,
  USA}, Department of Operations Research, University of Michigan, Ann Arbor,
  MI~48103, USA, April 1985.
\newblock See Murty \cite{ipm:Murty2,ipm:Murty3}.

\bibitem{ipm:Mylander1}
W.~C. Mylander, R.~L. Holmes, and G.~P. McCormick.
\newblock A guide to {SUMT--Version~4}\,: {The} computer program implementing
  the sequential unconstrained minimization technique for nonlinear
  programming.
\newblock {Research Paper} RAC--P--63, Research Analysis Corporation, McLean,
  USA, 1971.

\bibitem{ipm:Nakamura1}
Y.~Nakamura.
\newblock Lax pair and fixed point analysis of {Karmarkar's} projective scaling
  trajectory for linear programming.
\newblock {\em Japan Journal of Industrial and Applied Mathematics}, 11:1--9,
  1994.

\bibitem{ipm:Nash1}
S.~G. Nash.
\newblock Optimization at {ICIAM\,'91}.
\newblock {\em SIAM News}, 24(5):16, September 1991.

\bibitem{ipm:Nash4}
S.~G. Nash, R.~Polyak, and A.~Sofer.
\newblock A numerical comparison of barrier and modified barrier methods for
  large--scale bound--constrained optimization.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 319--338.
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Nash2}
S.~G. Nash and A.~Sofer.
\newblock Newton--type barrier methods for large--scale nonlinear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Operations Research and Applied Statistics, George Mason
  University, Fairfax, VA~22030, USA, April 1992.

\bibitem{ipm:Nash3}
S.~G. Nash and A.~Sofer.
\newblock A barrier method for large--scale constrained optimization.
\newblock {\em ORSA Journal on Computing}, 5:40--53, 1993.

\bibitem{ipm:Nash5}
S.~G. Nash and A.~Sofer.
\newblock On the complexity of a practical interior--point method.
\newblock {\em SIAM Journal on Optimization}, 8:833--849, 1998.

\bibitem{ipm:Nash6}
S.~G. Nash and A.~Sofer.
\newblock Why extrapolation helps barrier methods.
\newblock {Technical Report}, Department of Operations Research and Applied
  Statistics, George Mason University, Fairfax, VA~22030, USA, September 1998.

\bibitem{ipm:Nayakkankuppam1}
M.~V. Nayakkankuppam and M.~L. Overton.
\newblock Primal--dual interior--point methods for semidefinite programming.
\newblock In {\em Proceedings of the IEEE International Symposium on
  Computer--Aided Control System Design}, pages 235--239. IEEE Control Systems
  Society, September 1996.

\bibitem{ipm:Nazareth1}
J.~L. Nazareth.
\newblock Karmarkar's method and homotopies with restart.
\newblock {CDSS Report}, University of California, Berkeley, CA~94720, USA,
  1985.

\bibitem{ipm:Nazareth2}
J.~L. Nazareth.
\newblock Homotopy techniques in linear programming.
\newblock {\em Algorithmica}, 1(4):529--535, 1986.

\bibitem{ipm:Nazareth3}
J.~L. Nazareth.
\newblock Pricing criteria in linear programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 105--130. Springer Verlag, Berlin,
  Germany, 1989.

\bibitem{ipm:Nazareth4}
J.~L. Nazareth.
\newblock Some parallels in the historical development of the simplex and
  interior point methods for linear programming.
\newblock {\em {Mathematics Notes from Washington State University}}, 33(1),
  January 1990.

\bibitem{ipm:Nazareth8}
J.~L. Nazareth.
\newblock The duality principle and algorithms for linear programming\,: {A}
  unified approach based on quadratic and conic approximating models.
\newblock {Technical Report}, Department of Pure and Applied Mathematics,
  Washington State University, Pullman, WA~99164--3113, USA, June 1991.

\bibitem{ipm:Nazareth5}
J.~L. Nazareth.
\newblock The homotopy principle and algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 1(3):316--332, 1991.

\bibitem{ipm:Nazareth7}
J.~L. Nazareth.
\newblock Quadratic and conic approximating models in linear programming.
\newblock {Technical Report}, Department of Pure and Applied Mathematics,
  Washington State University, Pullman, WA~99164--3113, USA, May 1992.
\newblock Revised October 1992. To appear in {\em Mathematical Progamming
  Society Committee on Algorithms (COAL) Bulletin 23 (1994)}.

\bibitem{ipm:Nazareth10}
J.~L. Nazareth.
\newblock Trust regions based on conic functions in linear and nonlinear
  programming.
\newblock {Technical Report}, Department of Pure and Applied Mathematics,
  Washington State University, Pullman, WA~99164--3113, USA, October 1992.
\newblock Submitted to {\em Journal on Numerical Linear Algebra and
  Applications}.

\bibitem{ipm:Nazareth9}
J.~L. Nazareth.
\newblock From {Dikin} to {Karmarkar} via scalings, models and trust regions.
\newblock {\em SIAG/OPT Views--and--News, A Forum for the SIAM Activity Group
  on Optimization}, 1, 1993.

\bibitem{ipm:Nazareth11}
J.~L. Nazareth.
\newblock A reformulation of the central path equations and its algorithmic
  implications.
\newblock {Technical Report} 94--1, Department of Pure and Applied Mathematics,
  Washington State University, Pullman, WA~99164--3113, USA, September 1993.
\newblock Revised February 1994.

\bibitem{ipm:Nazareth13}
J.~L. Nazareth.
\newblock A framework for interior point methods of linear programming.
\newblock {\em Optimization Methods and Software}, 5:227--234, 1995.

\bibitem{ipm:Nazareth6}
J.~L. Nazareth.
\newblock The implementation of linear programming algorithms based on
  homotopies.
\newblock {\em Algorithmica}, 15:332--350, 1996.

\bibitem{ipm:Nazareth12}
J.~L. Nazareth.
\newblock Deriving potential functions via a symmetry principle for nonlinear
  equations.
\newblock {\em Operations Research Letters}, 21:147--152, 1997.

\bibitem{ipm:Nemhauser1}
G.~L. Nemhauser and L.~A. Wolsey.
\newblock {\em Integer and Combinatorial Optimization}, chapter I.6.4\,: {A}
  projective algorithm for linear programming, pages 164--172.
\newblock John Wiley\,\&\,Sons, New York, 1988.

\bibitem{ipm:Nemirovsky1}
A.~S. Nemirovsky.
\newblock An algorithm of the {Karmarkar} type.
\newblock {\em Teknicheskaya Kibernetika}, 1:105--118, 1987.
\newblock Translated in\,: {\em Soviet Journal on Computers and System
  Sciences~25(5):61--74, 1987}.

\bibitem{ipm:Nemirovsky2}
A.~S. Nemirovsky.
\newblock An new polynomial algorithm for linear programming.
\newblock {\em Doklady Akademii Nauk SSSR}, 298(6):1321--1325, 1988.
\newblock Translated in\,: {\em Soviet Mathematics Doklady~37(1): 264--269,
  1988}.

\bibitem{ipm:Nemirovsky4}
A.~S. Nemirovsky.
\newblock On polynomiality of the method of analytic centers for fractional
  problems.
\newblock {\em Mathematical Programming}, 73:175--198, 1996.

\bibitem{ipm:Nemirovsky7}
A.~S. Nemirovsky.
\newblock Polynomial time methods in convex programming.
\newblock In J.~Renegar, M.~Shub, and S.~Smale, editors, {\em The Mathematics
  of Numerical Analysis (1995 AMS--SIAM Summer Seminar in Applied Mathematics
  July/August 1995 held at Park City, UT, USA)}, volume~32 of {\em Lectures in
  Applied Mathematics}, pages 543--589. American Mathematical Society,
  Providence, RI~02940--6248, USA, 1996.

\bibitem{ipm:Nemirovsky6}
A.~S. Nemirovsky.
\newblock The long--step method of analytic centers for fractional problems.
\newblock {\em Mathematical Programming}, 77:191--224, 1997.

\bibitem{ipm:Nemirovsky9}
A.~S. Nemirovsky.
\newblock On normal self--concordant barriers and long--step interior point
  methods.
\newblock {Working Paper}, Optimization Laboratory Faculty of Industrial
  Engineering and Managament at Technion, Technion City, Haifa~32000, Israel,
  August 1997.

\bibitem{ipm:Nemirovsky8}
A.~S. Nemirovsky.
\newblock On self--concordant convex--concave functions.
\newblock {Research Report} 3/97, Optimization Laboratory Faculty of Industrial
  Engineering and Managament at Technion, Technion City, Haifa~32000, Israel,
  June 1997.

\bibitem{ipm:Nemirovsky5}
A.~S. Nemirovsky and P.~Gahinet.
\newblock The projective method for solving linear matrix inequalities.
\newblock {\em Proceedings of the American Control Conference (June 1994)},
  pages 840--844, 1994.

\bibitem{ipm:Nemirovsky10}
A.~S. Nemirovsky, C.~Roos, and T.~Terlaky.
\newblock On maximization of quadratic form over intersection of ellipsoids
  with common center.
\newblock {Technical Report} 98--??, Faculty of Technical Mathematics and
  Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft,
  The Netherlands, June 1998.

\bibitem{ipm:Nemirovsky3}
A.~S. Nemirovsky and K.~Scheinberg.
\newblock Extension of {Karmarkar's} algorithm onto convex quadratically
  constrained quadratic problems.
\newblock {\em Mathematical Programming}, 72:273--289, 1996.

\bibitem{ipm:Nering1}
E.~D. Nering and A.~W. Tucker.
\newblock {\em Linear Programs and Related Problems}, chapter 6.6\,: {The
  Karmarkar} algorithm, pages 241--249.
\newblock Academic Press, San Diego, CA, USA, 1993.

\bibitem{ipm:Nesterov1}
Yu.~E. Nesterov.
\newblock Polynomial methods in the linear and quadratic programming.
\newblock {\em Teknicheskaya Kibernetika}, 3:3--6, 1988.
\newblock Translated in\,: {\em Soviet Journal on Computers and System
  Sciences~26:98--101, 1988}.

\bibitem{ipm:Nesterov2}
Yu.~E. Nesterov.
\newblock Polynomial--time dual algorithms for linear programming.
\newblock {\em Kibernetika}, 25(1):34--40, 1989.
\newblock Translated in\,: {\em Cybernetics~25(1):40--49, 1989}.

\bibitem{ipm:Nesterov15}
Yu.~E. Nesterov.
\newblock Cutting plane algorithms from analytic centers\,: {Efficiency}
  estimates.
\newblock {Technical Report} 1992.?, Department of Economical and Social
  Sciences, University of Geneva, CH--1211 Geneva, Switzerland, 1992.

\bibitem{ipm:Nesterov11}
Yu.~E. Nesterov.
\newblock Long--step strategies in interior point potential--reduction methods.
\newblock {Technical Report}, Department of Management Studies, Faculty of SES,
  University of Geneva, Geneva, Switzerland, 1993.

\bibitem{ipm:Nesterov16}
Yu.~E. Nesterov.
\newblock Complexity estimates of some cutting plane methods based on the
  analytic barrier.
\newblock {\em Mathematical Programming}, 69:149--176, 1995.

\bibitem{ipm:Nesterov19}
Yu.~E. Nesterov.
\newblock Infeasible start interior point primal--dual methods in nonlinear
  programming.
\newblock {CORE Discussion Paper} 9567, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, 1995.

\bibitem{ipm:Nesterov23}
Yu.~E. Nesterov.
\newblock Interior--point methods\,: {An} old and new approach to nonlinear
  programming.
\newblock {\em Mathematical Programming}, 79:285--297, 1997.

\bibitem{ipm:Nesterov21}
Yu.~E. Nesterov.
\newblock Long--step strategies in interior--point primal--dual methods.
\newblock {\em Mathematical Programming}, 76:47--94, 1997.

\bibitem{ipm:Nesterov6}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock A general approach to polynolmial--time algorithms design for convex
  programming.
\newblock {Technical Report}, Central Economic and Mathematical Institute, USSR
  Academy of Science, Moscow, USSR, 1988.

\bibitem{ipm:Nesterov4}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock Self--concordant functions and polynomial--time methods in convex
  programming.
\newblock {Book--Preprint}, Central Economic and Mathematical Institute, USSR
  Academy of Science, Moscow, USSR, 1989.
\newblock Published in Nesterov and Nemirovsky \cite{ipm:Nesterov5}.

\bibitem{ipm:Nesterov18}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock Logarithmically homogeneous barriers and polynomial time methods
  based {Lyapunov's} functions.
\newblock {Research Report}, Central Economic and Mathematical Institute, USSR
  Academy of Science, Moscow, USSR, May 1990.

\bibitem{ipm:Nesterov9}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock Logarithmically homogeneous barriers and potential based polynomial
  time methods in convex programming.
\newblock {Research Report}, Central Economic and Mathematical Institute, USSR
  Academy of Science, Moscow, USSR, May 1990.

\bibitem{ipm:Nesterov3}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock Acceleration and parallelization of the path--following interior
  point method for a linearly constrained convex quadratic problem.
\newblock {\em SIAM Journal on Optimization}, 1(4):548--564, 1991.

\bibitem{ipm:Nesterov7}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock {'Conic'} formulation of a convex programming problem and duality.
\newblock {\em Optimization\,\&\,Software}, 1:10--31, 1992.

\bibitem{ipm:Nesterov5}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock {\em Interior--Point Polynomial Algorithms in Convex Programming\,:
  Theory and Algorithms}, volume~13 of {\em Studies in Applied Mathematics}.
\newblock Society of Industrial and Applied Mathematics (SIAM) Publications,
  Philadelphia, PA~19101, USA, 1993.

\bibitem{ipm:Nesterov8}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock An interior--point method for generalized linear--fractional
  programming.
\newblock {\em Mathematical Programming}, 69:177--204, 1995.

\bibitem{ipm:Nesterov20}
Yu.~E. Nesterov and A.~S. Nemirovsky.
\newblock Multi--parameter surfaces of analytic centers and long--step
  path--following interior point methods.
\newblock {\em Mathematics of Operations Research}, 23:1--38, 1998.

\bibitem{ipm:Nesterov14}
Yu.~E. Nesterov and A.~S. Nemorirovsky.
\newblock Technique for constructing self--concordant barriers.
\newblock {Technical Report} 1993.17, Department of Economical and Social
  Sciences, University of Geneva, CH--1211 Geneva, Switzerland, 1993.

\bibitem{ipm:Nesterov25}
Yu.~E. Nesterov, O.~Peton, and J.-Ph. Vial.
\newblock Homogeneous analytic center cutting plane methods with approximate
  centers.
\newblock {HEC Technical Report} 98.3, Department of Management Studies,
  UNiversity of Geneva, Geneva, The Switzerland, February 1998.

\bibitem{ipm:Nesterov24}
Yu.~E. Nesterov and M.~J. Todd.
\newblock Self-scaled cones and interior-point methods in nonlinear
  programming.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1994.

\bibitem{ipm:Nesterov10}
Yu.~E. Nesterov and M.~J. Todd.
\newblock Self--scaled barriers and interior--point methods for convex
  programming.
\newblock {\em Mathematics of Operations Research}, 22:1--42, 1997.
\newblock See also Nesterov and Todd \cite{ipm:Nesterov13}.

\bibitem{ipm:Nesterov13}
Yu.~E. Nesterov and M.~J. Todd.
\newblock Primal--dual interior--point methods for self--scaled cones.
\newblock {\em SIAM Journal on Optimization}, 8:324--364, 1998.
\newblock See also Nesterov and Todd \cite{ipm:Nesterov10}.

\bibitem{ipm:Nesterov17}
Yu.~E. Nesterov and M.~J. Todd.
\newblock Infeasible--start primal--dual methods and infeasible detectors for
  nonlinear programming.
\newblock {\em Mathematical Programming}, 84:227--267, 1999.

\bibitem{ipm:Nesterov22}
Yu.~E. Nesterov and J.-Ph. Vial.
\newblock Homogeneous analytic center cutting plane methods for convex problems
  and variational inequalities.
\newblock {Logilab Technical Report} 1997.4, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, 1997.

\bibitem{ipm:Nesterov12}
Yu.~E. Nesterov and Y.~Ye.
\newblock Polynomial methods in linear and quadratic programming.
\newblock {\em Soviet Journal of Computer and Systems Sciences}, 26(5):98--101,
  1988.

\bibitem{ipm:Neumann1}
{J. von} Neumann.
\newblock On a maximization problem.
\newblock Manuscript, Institute for Advanced Studies, Princeton University,
  Princeton, NJ 08544, USA, 1947.

\bibitem{ipm:Nickel1}
W.~Nickel, W.~R{\"o}dder, L.~Xu, and H.~J. Zimmermann.
\newblock Intelligent gradient search in linear programming.
\newblock {\em European Journal of Operational Research}, 22:293--303, 1985.

\bibitem{ipm:Nie1}
Y.~Nie and S.~Xu.
\newblock In isometric plane method for linear programming.
\newblock {\em Journal of Computational Mathematics}, 9(3):262--272, 1991.

\bibitem{ipm:Noma3}
T.~Noma.
\newblock {\em A globally convergent iterative algorithm for complementarity
  problems\,: {A} modification of interior point algorithms for linear
  complementarity problems}.
\newblock PhD thesis, Department of Information Science, Tokyo Institute of
  Technology, 2--12--1~Oh--Okayama, Meguro--ku, Tokyo~152, Japan, 1991.

\bibitem{ipm:Noma2}
T.~Noma and M.~Kojima.
\newblock A global, convergent iterative algorithm for complementarity
  problems.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Information Science, Tokyo Institute of
  Technology, 2--12--1~Oh--Okayama, Meguro--ku, Tokyo~152, Japan, July 1991.

\bibitem{ipm:Noma1}
T.~Noma, N.~Megiddo, M.~Kojima, and A.~Yoshise.
\newblock Some classes of linear complementarity problems that can be processed
  by interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Department of Information Science, Tokyo Institute of Technology,
  2--12--1~Oh--Okayama, Meguro--ku, Tokyo~152, Japan, October 1990.

\bibitem{ipm:Nunez1}
M.~A. Nunez.
\newblock Experiments using variants of {Dikin's} ellipsoid method for solving
  mathematical programs.
\newblock Master's thesis, Systems Optimization Laboratory, Department of
  Operations Research, Stanford University, Stanford, CA~94305, USA, 1990.

\bibitem{ipm:Nunez3}
M.~A. Nunez.
\newblock A characterization of ill--posed data instances for convex
  programming.
\newblock {Technical Report}, School of Business and Economics, Chapman
  University, 333~N~Glassell Street, Orange, CA~92866, USA, September 1998.

\bibitem{ipm:Nunez2}
M.~A. Nunez and R.~M. Freund.
\newblock Condition measures and properties of the central trajectory of a
  linear program.
\newblock {\em Mathematical Programming}, 83:1--28, 1998.
\newblock Identical version to Freund and Nunez \cite{ipm:Freund33}.

\bibitem{ipm:Nurminskii1}
E.~A. Nurminskii, S.~K. Andrusenko, and P.~I. Stetsyuk.
\newblock A new polynomial algorithm for linear programming.
\newblock {\em Kibernetika (Kiev)}, 4:118--120, 136, 1985.
\newblock (In Russian, English summary).

\bibitem{ipm:Obuchowska1}
W.~T. Obuchowska and R.~J. Caron.
\newblock Improving the rate of convergence of interior point methods for
  smooth convex programmes.
\newblock {\em Optimization}, 35:317--332, 1995.

\bibitem{ipm:Ohara1}
A.~Ohara.
\newblock Interior point methods and dual geometry in convex programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 889:19--25,
  1994.
\newblock (In Japanese). English journal\,: {\em Applied Analysis in Terms of
  Nonlinear Integrable Systems}, Kyoto, 1994.

\bibitem{ipm:Ohara2}
A.~Ohara.
\newblock Information geometric analysis of an interior--point method for
  semidefinite programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
  1004:71--89, 1997.

\bibitem{ipm:Oliveira1}
{A. R. L. de} Oliveira.
\newblock {\em A new class of preconditioners for large--scale linear systems
  for interior--point methods for linear programming}.
\newblock PhD thesis, Department of Computational and Applied Mathematics, Rice
  University, Houston, TX~77251, USA, 1997.
\newblock Available as\,: Technical Report TR97--11.

\bibitem{ipm:Oliviera3}
{A. R. L. de} Oliviera and D.~C. S{\o}rensen.
\newblock Computational experience with a preconditioner for interior point
  methods for linear programming.
\newblock {Technical Report} TR\,97--28, Department of Computational and
  Applied Mathematics, Rice University, Houston, TX~77251, USA, November 1997.

\bibitem{ipm:Oliviera2}
{A. R. L. de} Oliviera and D.~C. S{\o}rensen.
\newblock A new class of preconditioners for large--scale linear systems from
  interior point methods for linear programming.
\newblock {Technical Report} TR\,97--27, Department of Computational and
  Applied Mathematics, Rice University, Houston, TX~77251, USA, November 1997.

\bibitem{ipm:Oohori1}
T.~Oohori and A.~Ohuchi.
\newblock Symbolic generation of an optimal {Karmarkar's} algorithm for sparse
  linear programs.
\newblock In H.~J. Sebastian and K.~Tammer, editors, {\em System Modelling and
  Optimization\,: Proceedings of the 14th IFIP--Confernce, Leipzig,
  East--Germany, July 1989}, volume 143 of {\em Lecture Notes in Control and
  Information Sciences}, pages 194--203. Springer Verlag, Berlin, Germany,
  1990.

\bibitem{ipm:Osborne1}
M.~R. Osborne.
\newblock Dual barrier functions with superfast rates of convergence for the
  linear programming problem.
\newblock {\em Journal of the Australian Mathematical Society, Ser.\,B},
  29:39--58, 1987.

\bibitem{ipm:Osborne2}
M.~R. Osborne.
\newblock An interior point method for linear programming.
\newblock {\em Journal of the Australian Mathematical Society, Ser.\,B},
  31:367--378, 1990.

\bibitem{ipm:Osborne3}
M.~R. Osborne.
\newblock A modified barrier function method for linear programming.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 247--255. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Oestermark2}
R.~{\"O}stermark.
\newblock Polynomial convergence to the efficient set of polytopes by interior
  point methology\,: {Application} -- {Multiperiod} programming under risk.
\newblock {Meddelanden fran Ekonomisk--Statsvetenskapliga Fakulteten vid Abo
  Akademi, Series A} 324, Ekonomisk--Statsvetenskapliga Fakulteten, Abo
  University, Abo, Finland, 1991.

\bibitem{ipm:Oestermark3}
R.~{\"O}stermark.
\newblock Parametric stability of interior point methods for linear
  programming\,: {Evidence} on solving portfolio problems on hihgh performance
  computers.
\newblock {Meddelanden fran Ekonomisk--Statsvetenskapliga Fakulteten vid Abo
  Akademi, Series A} 360, Ekonomisk--Statsvetenskapliga Fakulteten, Abo
  University, Abo, Finland, 1992.

\bibitem{ipm:Oestermark1}
R.~{\"O}stermark.
\newblock Solving a linear multi--period portfolio problem by interior--point
  methodology.
\newblock {\em Computer Science in Economics and Management}, 5:283--302, 1992.

\bibitem{ipm:Oestermark4}
R.~{\"O}stermark and M.~Saarinen.
\newblock A multiprocessor interior point algorithm.
\newblock {\em Kybernetes}, 25:84--100, 1996.

\bibitem{ipm:Padberg1}
M.~W. Padberg.
\newblock Solution of a nonlinear programming problem arising in the projective
  method for linear programming.
\newblock {Technical Report}, School of Business and Administration, New York
  University, New York, NY~10003, USA, March 1985.
\newblock To appear in {\em SIAM Journal on Control and Optimization}.

\bibitem{ipm:Padberg2}
M.~W. Padberg.
\newblock A different convergence proof of the projective method for linear
  programming.
\newblock {\em Operations Research Letters}, 4:253--257, 1986.

\bibitem{ipm:Pai1}
R.~Pai, N.~K. Karmarkar, and {S. S.} S.~P. Rao.
\newblock A global router based on {Karmarkar's} interior point method.
\newblock {CSE Technical Report}, Indian Institute of Technology, Bombay,
  India, April 1988.

\bibitem{ipm:Pan1}
V.~Pan.
\newblock The modified barrier function method for linear programming and its
  extension.
\newblock {\em Computers and Mathematics with Applications}, 20(3):1--14, 1990.

\bibitem{ipm:Pan2}
V.~Pan and J.~Reif.
\newblock Efficient parallel linear programming.
\newblock {\em Operations Research Letters}, 5:127--135, 1986.

\bibitem{ipm:Pan3}
V.~Pan and J.~Reif.
\newblock Fast and efficient linear programming and linear least--squares
  computations.
\newblock {\em Computers and Mathematics with Applications Ser.~A},
  12:1217--1227, 1986.

\bibitem{ipm:Panik1}
M.~J. Panik.
\newblock {\em {Linear Programming\,: Mathematics, Theory and Algorithms}},
  volume~2 of {\em Applied Optimization}, chapter 13\,: {Interior} point
  methods, chapter 14\,: {Interior} point algorithms for solving linear
  complementary problems, pages 341--458.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995.

\bibitem{ipm:ParadaGarcia1}
Z.~{Parada Gracia}.
\newblock {\em A modified augmented {Lagrangian} merit function, and
  q--superlinear characterization results for primal--dual quai--{Newton}
  interior--point methods for nonlinear programming}.
\newblock PhD thesis, Department of Computational and Applied Mathematics, Rice
  University, Houston, TX~77251, USA, 1997.
\newblock Available as\,: Technical Report TR97--12.

\bibitem{ipm:Pardalos1}
P.~M. Pardalos.
\newblock Interior point algorithms for nonconvex quadratic problems.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Department
  of Computer Science, Pennsylvania State University, University Park,
  PA~16802, USA, August 1990.

\bibitem{ipm:Pardalos6}
P.~M. Pardalos.
\newblock Polynomial time algorithms for some classes of constrained nonconvex
  quadratic problems.
\newblock {\em Optimization}, 21:843--853, 1990.

\bibitem{ipm:Pardalos12}
P.~M. Pardalos.
\newblock The linear complementarity problem.
\newblock In S.~Gomez and J.~P. Hennart, editors, {\em Advances in Optimization
  and Numerical Analysis (Proceedings of the Sixth Workshop on Optimization and
  Numerical Analysis, Oaxaca, Mexico, 1992)}, volume 275 of {\em Mathematics
  and Its Applications}, pages 39--49. Kluwer Academic Publishers, Dordrecht,
  The Netherlands, 1994.

\bibitem{ipm:Pardalos7}
P.~M. Pardalos, C.~G. Han, J.~A. Kaliski, and Y.~Ye.
\newblock Solution of quadratic programming and linear complementarity problems
  using a potential reduction algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Computer Science, Pennsylvania State
  University, University Park, PA~16802, USA, May 1991.

\bibitem{ipm:Pardalos2}
P.~M. Pardalos, C.~G. Han, and Y.~Ye.
\newblock Computational aspects of an interior point algorithm for quadratic
  problems with box constraints.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Department of Computer Science, Pennsylvania State University, University
  Park, PA~16802, USA, July 1990.

\bibitem{ipm:Pardalos9}
P.~M. Pardalos, C.~G. Han, and Y.~Ye.
\newblock Interior--point algorithms for solving nonlinear optimization
  problems.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:45--54, August 1991.

\bibitem{ipm:Pardalos10}
P.~M. Pardalos and M.~G.~C. Resende.
\newblock Interior point algorithms for network flow problems.
\newblock In J.~E. Beasley, editor, {\em Advances in Linear and Nonlinear
  Programming}, pages 145--185. Oxford University Press, Oxford, Great Britain,
  1995.
\newblock Identical to Resende and Pardalos\,\cite{ipm:Resende19}.

\bibitem{ipm:Pardalos11}
P.~M. Pardalos and M.~G.~C. Resende.
\newblock Interior point methods for global optimization.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 467--500. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Pardalos5}
P.~M. Pardalos, Y.~Ye, and C.~G. Han.
\newblock An interior point algorithm for large--scale quadratic problems with
  box constraints.
\newblock In A.~Bensoussan and J.~L. Lions, editors, {\em Analysis and
  Optimization of Systems\,: Proceedings of the 9th International Conference,
  Antibes, France, 1990}, volume 144 of {\em Lecture Notes in in Control and
  Information Sciences}, pages 413--422. Springer Verlag, Berlin, Germany,
  1990.

\bibitem{ipm:Pardalos3}
P.~M. Pardalos, Y.~Ye, and C.~G. Han.
\newblock Parallel computing in quadratic programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department Computer Science, Pennsylvania State University, University
  Park, PA~16802, USA, May 1990.

\bibitem{ipm:Pardalos4}
P.~M. Pardalos, Y.~Ye, and C.~G. Han.
\newblock Algorithms for the solution of quadratic knapsack problems.
\newblock {\em Linear Algebra and Its Applications}, 152:69--91, 1991.

\bibitem{ipm:Pardalos13}
P.~M. Pardalos, Y.~Ye, and C.~G. Han.
\newblock Interior point algorithms in quadratic programming.
\newblock In V.~P. Bulatov, editor, {\em {Optimizatsiya\,: Modeli, Metody,
  Resheniya}}, pages 194--213. Nauka, Novosibirsk, USSR, 1992.

\bibitem{ipm:Pardalos8}
P.~M. Pardalos, Y.~Ye, C.~G. Han, and J.~A. Kaliski.
\newblock Solution of {$P_{0}$}--matrix linear complementarity problems using a
  potential reduction algorithm.
\newblock {\em SIAM Journal on Matrix Analysis and Applications},
  14:1048--1060, 1993.

\bibitem{ipm:Paris1}
Q.~Paris.
\newblock A primer on {Karmarkar's} algorithm for linear programming.
\newblock {\em METU Studies in Develpoment}, 12(1--2):131--155, 1985.

\bibitem{ipm:Parisot1}
G.~R. Parisot.
\newblock Resolution numerique approchee du probleme de programmation lineaire
  par application de la programmation logarithmique {(Approximate numerical
  solution of linear programming problems by an application of the logarithmic
  programming)}.
\newblock {\em Revue Francaise Recherche Operationelle}, 20:227--259, 1961.
\newblock (In French).

\bibitem{ipm:Parker1}
R.~G. Parker and R.~L. Rardin.
\newblock {\em Discrete Optimization}, chapter 4.1.3\,: {Karmarkar's}
  projection scaling algorithm, pages 117--131.
\newblock Academic Press, New York, NY, USA, 1988.

\bibitem{ipm:Pataki1}
G.~Pataki and L.~Tun{\c{c}}el.
\newblock On the generic properties of convex optimization problems in conic
  form.
\newblock {Reseach Report} CORR\,97--16, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada,
  September 1997.

\bibitem{ipm:Pena3}
J.~Pe{\~{n}}a.
\newblock Computing the distance to infeasibility\,: {Theoretical} and
  practical issues.
\newblock {Technical Report}, Center for Applied Mathematics, Cornell
  University, Ithaca, NY~14853, USA, October 1997.

\bibitem{ipm:Pena2}
J.~Pe{\~{n}}a.
\newblock Understanding the geometry of infeasible perturbations of a conic
  linear system.
\newblock Manuscript, Computational and Applied Mathematics Program, Cornell
  University, Ithaca, NY~14853, USA, June 1997.

\bibitem{ipm:Pena1}
J.~Pe{\~{n}}a and J.~Renegar.
\newblock Quickly computing backward--approximate solutions for
  ill--conditioned systems of linear inequalities and forward--approximate
  solutions for well--conditioned systems.
\newblock Manuscript, Computational and Applied Mathematics Program, Cornell
  University, Ithaca, NY~14853, USA, June 1997.

\bibitem{ipm:Peng1}
J.-M. Peng, C.~Roos, and T.~Terlaky.
\newblock New complexity analysis of the primal--dual {Newton} method for
  linear optimization.
\newblock {Technical Report} 98--05, Optimization Group TU Delft, Faculty of
  Information Technology and Systems, Delft University of Technology, P.O.\,Box
  5031, NL--2600~GA~Delft, The Netherlands, 1998.

\bibitem{ipm:Philpott1}
A.~B. Philpott.
\newblock Linear programming made simpler than simplex.
\newblock {\em New Scientist}, page~20, December 6, 1984.

\bibitem{ipm:Pickel1}
P.~F. Pickel.
\newblock Approximate projections for the {Karmarkar} algorithm.
\newblock Manuscript, Polytechnic Institute of New York, Farmingdale, NY, USA,
  1985.

\bibitem{ipm:Pickel2}
P.~F. Pickel.
\newblock Implementing the {Karmarkar} algorithm using simplex techniques.
\newblock {Talk held at the 12th International Symposium on Mathematical
  Programming in Cambridge, MA, USA}, Polytechnic Institute of New York,
  Farmingdale, NY, USA, 1985.

\bibitem{ipm:Pickel3}
P.~F. Pickel.
\newblock Preliminary computational experience with approximate projections in
  the {Karmarkar} algorithm.
\newblock {Technical Report}, Polytechnic Institute of New York, Farmingdale,
  NY, USA, 1986.

\bibitem{ipm:Plantenga1}
T.~Plantenga.
\newblock A trust region method for nonlinear programming based on primal
  interior--point techniques.
\newblock {\em SIAM Journal on Scientific Computing}, 20:282--305, 1998.

\bibitem{ipm:Polak1}
E.~Polak, J.~E. Higgins, and D.~Q. Mayne.
\newblock A barrier function method for minimax problems.
\newblock {\em Mathematical Programming}, 54:155--176, 1992.

\bibitem{ipm:Polak2}
E.~Polak, T.~H. Yang, and D.~Q. Mayne.
\newblock A method of centers based on barrier functions for solving optimal
  control problems with continuum state and control constraints.
\newblock In {\em Proceedings of the 29th Conference on Decision and Control},
  pages 2327--2332. IEEE Control Society, December 1990.

\bibitem{ipm:Polyak9}
R.~Polyak.
\newblock Classical lagrangians with properties of the augmented lagrangians.
\newblock {Talk held at the 12th International Symposium on Mathematical
  Programming in Boston, MA, USA}, Mathematical Sciences Department,
  IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598, USA, 1985.

\bibitem{ipm:Polyak19}
R.~Polyak.
\newblock Some problems of modern optimization theory and multipliers methods.
\newblock {Technical Report}, Znania, Kiev, 1985.
\newblock (In Russian).

\bibitem{ipm:Polyak18}
R.~Polyak.
\newblock Exterior and interior modified distance functions.
\newblock {Technical Report}, Viniti, Moscow, 1986.
\newblock (In Russian).

\bibitem{ipm:Polyak17}
R.~Polyak.
\newblock Modified barrier functions as augmented lagrangians.
\newblock {Technical Report}, Viniti, Moscow, 1986.
\newblock (In Russian).

\bibitem{ipm:Polyak6}
R.~Polyak.
\newblock Modified barrier and center methods.
\newblock {\em Reports from the Moscow Refusnik Seminar, Annals of the New York
  Academy of Sciences}, 491:194--196, 1987.

\bibitem{ipm:Polyak10}
R.~Polyak.
\newblock Monotone transformation in linear and nonlinear programming.
\newblock {Talk held at the Summer Conference ''Mathematical Developments
  Arising from Linear Programming'' in Bowdoin College, Brunswick, Maine, USA},
  Mathematical Sciences Department, IBM~T.\,J.\,Watson Research Center,
  Yorktown Heights, NY~10598, USA, June 1988.

\bibitem{ipm:Polyak11}
R.~Polyak.
\newblock Modified interior centers methods.
\newblock {Talk held at the Third SIAM Conference on Optimization in Boston,
  MA, USA}, Mathematical Sciences Department, IBM~T.\,J.\,Watson Research
  Center, Yorktown Heights, NY~10598, USA, April 1989.

\bibitem{ipm:Polyak5}
R.~Polyak.
\newblock The nonlinear rescaling principle in linear programming.
\newblock {Technical Report} RC~15030~(67093), Mathematical Sciences
  Department, IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598,
  USA, 1989.

\bibitem{ipm:Polyak12}
R.~Polyak.
\newblock Simultaneuos solution of the dual pair of nonlinear programming
  problems based on the modified barrier function.
\newblock {Talk held at the SIAM Annual Meeting in San Diego, CA, USA},
  Mathematical Sciences Department, IBM~T.\,J.\,Watson Research Center,
  Yorktown Heights, NY~10598, USA, 1989.

\bibitem{ipm:Polyak2}
R.~Polyak.
\newblock Interior point methods, nonlinear and parallel optimization.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Mathematical Sciences Department, IBM~T.\,J.\,Watson Research Center,
  Yorktown Heights, NY~10598, USA, July 1990.

\bibitem{ipm:Polyak1}
R.~Polyak.
\newblock Modified interior distance functions as augmented lagrangians.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Mathematical Sciences Department, IBM~T.~J.~Watson Research
  Center, Yorktown Heights, NY~10598, USA, January 1990.

\bibitem{ipm:Polyak16}
R.~Polyak.
\newblock Newton modified barrier method in constrained optimization.
\newblock In {\em Proceedings of the Air Force/NASA Symposium on Recent
  Advances in Multidisciplinary Analysis and Optimization, San Francisco,
  1990}. 1990.

\bibitem{ipm:Polyak13}
R.~Polyak.
\newblock Nonlinear rescaling principle in constrained optimization.
\newblock {Talk held at the International Congress of Mathematicians in Kyoto,
  Japan}, Mathematical Sciences Department, IBM~T.\,J.\,Watson Research Center,
  Yorktown Heights, NY~10598, USA, 1990.

\bibitem{ipm:Polyak14}
R.~Polyak.
\newblock Interior augmented lagrangians.
\newblock {Talk held at the 14th International Symposium on Mathematical
  Programming in Amsterdam, The Netherlands}, Mathematical Sciences Department,
  IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598, USA, August
  1991.

\bibitem{ipm:Polyak8}
R.~Polyak.
\newblock Modified interior distance functions and center methods.
\newblock {Research Report} 17042~(75556), IBM Research Division T.\,J.\,Watson
  Research Center, Yorktown Heights, NY~10598, USA, 1991.

\bibitem{ipm:Polyak15}
R.~Polyak.
\newblock Condition of the primal and dual linear programming problems.
\newblock {Talk held at the International Workshop on Computational
  Optimization in Haifa, Israel}, Mathematical Sciences Department,
  IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598, USA, 1992.

\bibitem{ipm:Polyak4}
R.~Polyak.
\newblock Modified barrier functions in linear programming.
\newblock {Research Report} 17790~(78331), Mathematical Sciences Department,
  IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598, USA, 1992.

\bibitem{ipm:Polyak3}
R.~Polyak.
\newblock Modified barrier functions (theory and methods).
\newblock {\em Mathematical Programming}, 54:177--222, 1992.

\bibitem{ipm:Polyak20}
R.~Polyak.
\newblock Modified interior distance functions.
\newblock In S.~Cox et~al., editor, {\em Optimzation Methods in Partial
  Differential Equations (Proceedings from the 1996 Joint Summer Research
  Conference, South Hadley, MA, USA, June 1996)}, volume 209 of {\em
  Contemporary Mathematics}, pages 183--209. American Mathematical Society,
  Providence, RI, USA, 1997.

\bibitem{ipm:Polyak7}
R.~Polyak and R.~R. Schneur.
\newblock Interior--exterior augmented {Lagrangian} approach for {LP}.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Mathematical Sciences Department, IBM~T.\,J.\,Watson Research
  Center, Yorktown Heights, NY~10598, USA, May 1992.

\bibitem{ipm:Ponceleon1}
D.~B. Poncele{\'o}n.
\newblock {\em Barrier methods for large--scale quadratic programming}.
\newblock PhD thesis, Computer Science Department, Stanford University,
  Stanford, CA~94305, USA, 1990.

\bibitem{ipm:Ponceleon2}
D.~B. Poncele{\'o}n.
\newblock Barrier methods for large--scale quadratic programming.
\newblock {Technical Report} SOL~91--2, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, June 1991.

\bibitem{ipm:Ponnambalam1}
K.~Ponnambalam.
\newblock Large scale nonlinear programming using interior point and successive
  linear programming methods.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, Faculty
  of Engineering, Department of Electrical Engineering, University of Waterloo,
  Waterloo, Ontario~N2L~3G1, Canada, July 1990.

\bibitem{ipm:Ponnambalam5}
K.~Ponnambalam.
\newblock An interior point algorithm for large scale nonlinear programming.
\newblock {Talk held at the Symposium APMOD\,'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Faculty of Engineering, Department of Electrical Engineering, University of
  Waterloo, Waterloo, Ontario~N2L~3G1, Canada, January 1991.

\bibitem{ipm:Ponnambalam10}
K.~Ponnambalam.
\newblock An interior point algorithm for large scale nonlinear programming.
\newblock {Technical Report}, Department of Systems Design Engineering,
  University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1992.

\bibitem{ipm:Ponnambalam11}
K.~Ponnambalam, V.~H. Quintana, and A.~Vannelli.
\newblock A fast algorithm for power system optimization problems using an
  interior point method.
\newblock {\em IEEE Transactions on Power Systems}, 7:892--899, 1992.

\bibitem{ipm:Ponnambalam6}
K.~Ponnambalam, S.~Seetharaman, and T.~Alguindigue.
\newblock Affine algorithms for {$L$}--minimization.
\newblock In {\em Proceedings of the Sixth Multidimensional Signal Processing
  Workshop held in Pacific Grove, CA, USA, September 1989}, page 115. IEEE, New
  York, NY, USA, 1989.

\bibitem{ipm:Ponnambalam2}
K.~Ponnambalam and A.~Vannelli.
\newblock New starting and stopping steps for the dual affine variant of
  {Karmarkar's} method.
\newblock {Technical Report}, Faculty of Engineering, Department of Electrical
  Engineering, University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1988.

\bibitem{ipm:Ponnambalam3}
K.~Ponnambalam and A.~Vannelli.
\newblock An inexpensive basis recovery procedure for {Karmarkar's} dual affine
  method.
\newblock {Technical Report}, Faculty of Engineering, Department of Electrical
  Engineering, University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1989.

\bibitem{ipm:Ponnambalam9}
K.~Ponnambalam and A.~Vannelli.
\newblock Forcing a vertex optimal solution in interior point methods using an
  auxiliary function.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD\,'93), Budapest, Hungary, January 1993,
  Volume of Extended Abstracts}, pages 463--470. Computer and Automation
  Institute, Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Ponnambalam8}
K.~Ponnambalam, A.~Vannelli, E.~A. McBean, and T.~E. Unny.
\newblock Solving large--scale electric energy production planning and
  pollution control problems with {Karmarkar} algorithms.
\newblock In G.~B. Dantzig and P.~Glynn, editors, {\em Proceedings of the
  Workshop on Resource Planning Under Uncertainty for Electric Power Systems
  held at Stanford University, January 1989}, pages 179--196. 1989.

\bibitem{ipm:Ponnambalam4}
K.~Ponnambalam, A.~Vannelli, and T.~E. Unny.
\newblock An application of {Karmarkar's} interior point linear programming
  algorithm for multi--reservoir operations optimization.
\newblock {\em Stochastic Hydrology and Hydraulics}, 3:17--29, 1992.

\bibitem{ipm:Ponnambalam7}
K.~Ponnambalam, A.~Vannelli, and S.~Woo.
\newblock An interior point method implementation for solving large planning
  problems in the oil refinery industry.
\newblock {\em Canadian Journal of Chemical Engineering}, 70:368--374, 1992.

\bibitem{ipm:Poore1}
A.~B. Poore and D.~Soria.
\newblock Continuation algorithms for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New Orleans,
  USA}, Department of Mathematics, Colorado State University, Fort Collins,
  CO~80253, USA, May 1987.

\bibitem{ipm:Portnoy1}
S.~Portnoy and R.~Koenker.
\newblock The {Gaussian Hare} and the {Laplacian Tortoise}\,: {Computability}
  of squared--error vs. absolute--error estimates.
\newblock {Technical Report}, Department of Statistics, University of Illinois
  at Urbana--Champaign, Urbana, Il~61820, USA, March 1997.

\bibitem{ipm:Portugal3}
L.~F. Portugal, F.~Bastos, J.~J. J{\'u}dice, J.~Paix{\~a}o, and T.~Terlaky.
\newblock An investigation of interior point algorithms for the linear
  transportation problem.
\newblock {\em SIAM Journal on Scientific Computing}, 17:1202--1223, 1996.

\bibitem{ipm:Portugal5}
L.~F. Portugal, L.~Fernandes, and J.~J. J{\'u}dice.
\newblock A truncated {Newton} interior--point algorithm for the solution of a
  multicommodity spatial equilibrium model.
\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
  Variational Problems\,: State--of--the--Art (Baltimore 1995)}, pages
  315--344. SIAM Publications, Philadelphia, PA, USA, 1997.

\bibitem{ipm:Portugal4}
L.~F. Portugal and J.~J. J{\'u}dice.
\newblock A hybrid algorithm for the solution of a single commodity spatial
  equilibrium model.
\newblock {Technical Report}, Department of Mathematics, University of Coimbra,
  Coimbra, Portugal, 1994.

\bibitem{ipm:Portugal1}
L.~F. Portugal, J.~J. J{\'u}dice, and L.~Vicente.
\newblock A comparison of block pivoting and interior--point algorithms for
  linear least squares problems with nonnegative variables.
\newblock {\em Mathematics of Computation}, 63:625--643, 1994.

\bibitem{ipm:Portugal2}
L.~F. Portugal, M.~G.~C. Resende, G.~Veiga, and J.~J. J{\'u}dice.
\newblock A truncated primal--infeasible dual--feasible network interior point
  method.
\newblock {Technical Report}, Mathematical Sciences Research Center, AT~\&~T
  Bell Laboratories, Murray Hill, NJ~07974--0636, USA, 1994.
\newblock Revised August 1996.

\bibitem{ipm:Potra2}
F.~A. Potra.
\newblock Implementation of interior point methods on parallel and vector
  machines.
\newblock In P.~Gritzmann, R.~Hettich, R.~Horst, and E.~Sachs, editors, {\em
  Operations Research '91 (Extended Abstracts of the 16th Symposium on
  Operations Research held at the University of Trier, Germany, September
  1991)}, pages 179--181. Springer Verlag, Berlin, Germany, 1992.

\bibitem{ipm:Potra8}
F.~A. Potra.
\newblock On a predictor--corrector method for solving linear programs from
  infeasible starting points.
\newblock {Reports on Computational Mathematics}~34, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, October 1992.
\newblock See also Potra \cite{ipm:Potra11}, which is a combined version of
  Potra \cite{ipm:Potra7} and this entry.

\bibitem{ipm:Potra4}
F.~A. Potra.
\newblock Polynomial complexity versus fast local convergence for interior
  point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Management Sciences, The University of Iowa, Iowa
  City, IA~52242, USA, May 1992.

\bibitem{ipm:Potra7}
F.~A. Potra.
\newblock A quadratically convergent infeasible interior--point algorithm for
  linear programming.
\newblock {Reports on Computational Mathematics}~28, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, July 1992.
\newblock See also Potra \cite{ipm:Potra11}, which is a combined version of
  this entry and Potra \cite{ipm:Potra8}.

\bibitem{ipm:Potra11}
F.~A. Potra.
\newblock A quadratically convergent predictor--corrector method for solving
  linear programs from infeasible starting points.
\newblock {\em Mathematical Programming}, 67:383--406, 1994.
\newblock This is a combined version of Potra \cite{ipm:Potra7,ipm:Potra8}.

\bibitem{ipm:Potra6}
F.~A. Potra.
\newblock An infeasible interior--point predictor--corrector algorithm for
  linear programming.
\newblock {\em SIAM Journal on Optimization}, 6:19--32, 1996.

\bibitem{ipm:Potra14}
F.~A. Potra.
\newblock An {$O(n\,L)$} infeasible--interior--point algorithm for {LCP} with
  quadratic convergence.
\newblock {\em Annals of Operations Research}, 62:81--102, 1996.

\bibitem{ipm:Potra12}
F.~A. Potra and J.~F. Bonnans.
\newblock Infeasible path following algorithms for linear complementarity
  problems.
\newblock {INRIA Research Report} RR--2445, Institute National de Recherche en
  Informatique et Automatique (INRIA), F--78153~Roquencourt, France, December
  1994.
\newblock To appear in {\em Mathematics of Operations Research}. See also
  Bonnans and Potra \cite{ipm:Bonnans6}.

\bibitem{ipm:Potra17}
F.~A. Potra and R.~Sheng.
\newblock Homogeneous interior--point algorithms for semidefinite programming.
\newblock {Reports on Computational Mathematics}~82, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, November 1995.

\bibitem{ipm:Potra15}
F.~A. Potra and R.~Sheng.
\newblock A path--following method for {LCP} with superlinearly convergent
  iteration sequence.
\newblock {Reports on Computational Mathematics}~69, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, April 1995.

\bibitem{ipm:Potra21}
F.~A. Potra and R.~Sheng.
\newblock Superlinear convergence of a predictor--corrector method for
  semidefinite programming without central path neighborhood.
\newblock {Reports on Computational Mathematics}~91, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, August 1996.

\bibitem{ipm:Potra18}
F.~A. Potra and R.~Sheng.
\newblock Superlinear convergence of interior--point algorithms for
  semidefinite programming.
\newblock {Reports on Computational Mathematics}~86, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, April 1996.

\bibitem{ipm:Potra13}
F.~A. Potra and R.~Sheng.
\newblock A large--step infeasible--interior--point method for the
  {$P_{*}$}--matrix {LCP}.
\newblock {\em SIAM Journal on Optimization}, 7:318--335, 1997.

\bibitem{ipm:Potra19}
F.~A. Potra and R.~Sheng.
\newblock Predictor--corrector algorithms for solving $p_{*}(\kappa)$--matrix
  {LCP} from arbitrary positive starting points.
\newblock {\em Mathematical Programming}, 76:223--244, 1997.

\bibitem{ipm:Potra23}
F.~A. Potra and R.~Sheng.
\newblock On homogeneous interior--point algorithms for semidefinite
  programming.
\newblock {\em Optimization Methods and Software}, 9:161--184, 1998.

\bibitem{ipm:Potra22}
F.~A. Potra and R.~Sheng.
\newblock Superlinearly convergent infeasible--interior--point algorithm for
  degenerate {LCP}.
\newblock {\em Journal of Optimization Theory and Applications}, 97:249--269,
  1998.

\bibitem{ipm:Potra16}
F.~A. Potra and R.~Sheng.
\newblock A superlinearly convergent primal--dual infeasible--interior--point
  algorithm for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:1007--1028, 1998.

\bibitem{ipm:Potra20}
F.~A. Potra, R.~Sheng, and N.~Brixius.
\newblock {SDPHA\,: A MATLAB} implementation of homogeneous interior--point
  algorithms for semidefinite programming.
\newblock {Reports on Computational Mathematics} 100, Department of
  Mathematics, The University of Iowa, Iowa City, IA~52242, USA, April 1997.

\bibitem{ipm:Potra9}
F.~A. Potra and Y.~Shi.
\newblock On an efficient interior point method for solving entropy
  optimization problems.
\newblock {Reports on Computational Mathematics}~23, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, December 1991.

\bibitem{ipm:Potra3}
F.~A. Potra, R.~A. Tapia, and Y.~Zhang.
\newblock An interior--point method for linear complementarity problems with
  polynomial complexity and superlinear convergence.
\newblock {Technical Report} TR~91--23, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Potra5}
F.~A. Potra and Y.~Ye.
\newblock An interior--point algorithm for solving entropy optimization
  problems with globally linear and locally quadratic convergence.
\newblock {Working Paper} 90--10, Department of Management Sciences, The
  University of Iowa, Iowa City, IA~52242, USA, 1990.
\newblock See also Potra and Ye\,\cite{ipm:Potra10}.

\bibitem{ipm:Potra1}
F.~A. Potra and Y.~Ye.
\newblock Interior point methods for nonlinear complementarity problems.
\newblock {Reports on Computational Mathematics}~15, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, July 1991.

\bibitem{ipm:Potra10}
F.~A. Potra and Y.~Ye.
\newblock A quadratically convergent polynomial algorithm for solving entropy
  optimization problems.
\newblock {\em SIAM Journal on Optimization}, 3:843--860, 1993.
\newblock See also Potra and Ye\,\cite{ipm:Potra5}.

\bibitem{ipm:Powell9}
M.~J. Powell.
\newblock Log barrier methods for semi--infinite programming calculations.
\newblock In {\em Hellenic Research in Mathematics and Informatics\,'92}, pages
  23--43. Hellenic Mathematical Society, Athens, Greece, 1992.
\newblock See also Powell \cite{ipm:Powell7}.

\bibitem{ipm:Powell2}
M.~J.~D. Powell.
\newblock Karmarkar's algorithm\,: {A} view from nonlinear programming.
\newblock {\em Bulletin of the Institute of Mathematics and Its Applications},
  26(8--9):165--181, 1990.

\bibitem{ipm:Powell1}
M.~J.~D. Powell.
\newblock Is {Karmarkar's} method suitable for semi--infinite programming\,?
\newblock {Talk held at the Symposium APMOD\,'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Department of Applied Mathematics and Theoretical Physics, University of
  Cambridge, Silver Street, Cambridge~CB3~9EW, United Kingdom, January 1991.
\newblock There is no underlying report.

\bibitem{ipm:Powell3}
M.~J.~D. Powell.
\newblock The complexity of {Karmarkar's} algorithm for linear programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
  1991}, volume 260 of {\em Pitman Research Notes in Mathematics}, pages
  142--163. Longman, Burnt Hill, Harlow, Essex, United Kingdom, 1992.

\bibitem{ipm:Powell5}
M.~J.~D. Powell.
\newblock Interior point methods for semi--infinite programming calculations.
\newblock In K.~H. Phua, C.~M. Wang, W.~Y. Yeong, T.~Y. Leong, H.~T. Loh, K.~C.
  Tan, and F.~S. Chou, editors, {\em Optimization\,: Techniques and
  Applications, Vol.\,1 (Proceedings of the International Conference (ICOTA)
  held in Singapore 1992)}, pages 3--5. World Science Publishing, River Edge,
  NJ, USA, 1992.

\bibitem{ipm:Powell6}
M.~J.~D. Powell.
\newblock Some convergence properties of the shifted log barrier method for
  linear programming.
\newblock {Technical Report} DAMTP~1992/NA7, Department of Applied Mathematics
  and Theoretical Physics, University of Cambridge, Silver Street,
  Cambridge~CB3~9EW, United Kingdom, November 1992.
\newblock Revised January 1994. See also Powell \cite{ipm:Powell8}.

\bibitem{ipm:Powell7}
M.~J.~D. Powell.
\newblock Log barrier methods for semi--infinite programming calculations.
\newblock In E.~A. Lipitakis, editor, {\em Advances on Computer Mathematics and
  Its Applications}, pages 1--21. World Scientific, Singapore, 1993.
\newblock See also Powell \cite{ipm:Powell9}.

\bibitem{ipm:Powell4}
M.~J.~D. Powell.
\newblock On the number of iterations of {Karmarkar's} algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 62:153--197, 1993.

\bibitem{ipm:Powell8}
M.~J.~D. Powell.
\newblock Some convergence properties of the modified log barrier method for
  linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:695--739, 1995.
\newblock See also Powell \cite{ipm:Powell6}.

\bibitem{ipm:Puthenpura1}
S.~Puthenpura, R.~Saigal, and L.~P. Sinha.
\newblock Application of the {LQ} factorization in implementing the {Karmarkar}
  algorithm and its variants.
\newblock {Technical Memorandum} 51173--900205--01TM, AT \& T Bell
  Laboratories, 1990.

\bibitem{ipm:Puthenpura2}
S.~Puthenpura, L.~Sinha, S.-C. Fang, and R.~Saigal.
\newblock Solving stochastic programming problems via {Kalman} filter and
  affine scaling.
\newblock {\em European Journal of Operational Research}, 83:503--513, 1995.

\bibitem{ipm:Puzanova1}
E.~A. Puzanova.
\newblock Allowance for error in computer computations in the {Karmarkar}
  method.
\newblock {\em Optimizatsiya}, 46(63):51--67, 1989.
\newblock (In Russian).

\bibitem{ipm:Qi1}
L.~Qi and J.~Sun.
\newblock A nonsmooth version of {Newton's} method and an interior point
  algorithm for convex programming.
\newblock {Technical Report} 90--01, Department of Industrial Engineering and
  Management Science, Northwestern University, Evanston, IL~60208, USA, 1990.

\bibitem{ipm:Qi2}
R.-J. Qi and S.~A. Zenios.
\newblock On the scalability of data--parallel decomposition algorithms for
  stochastic programming.
\newblock {\em Journal of Parallel and Distributed Computing}, 22:565--570,
  1994.

\bibitem{ipm:Qualm1}
M.~J. Qualm.
\newblock Interior point methods and integer programming problems.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2628~CD~Delft, The Netherlands, 1993.

\bibitem{ipm:Quintana1}
V.~H. Quintana, A.~Vannelli, and K.~Ponnambalam.
\newblock A fast dual affine implementation for power optimization.
\newblock {\em IEEE Transactions on Power Systems}, 7:892--899, 1992.

\bibitem{ipm:Quist1}
A.~J. Quist, {E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Copositive relaxation for general quadratic programming.
\newblock {\em Optimization Methods and Software}, 9:185--208, 1998.

\bibitem{ipm:Radosavljevic1}
M.~D. Radosavljevi{\'c}-Nicoli{\'c}.
\newblock Asymptotic behavior of the affine scaling variant of {Karmarkar's}
  algorithm for linear programming.
\newblock In {\em Proceedings of the XX--th Conference 'Mathematical
  Optimization', Humboldt Universit{\"a}t Berlin, East--Germany}. 1990.

\bibitem{ipm:Rajan1}
A.~Rajan.
\newblock An empirical comparison of {KORBX} against {RELAXT}, a special code
  for network flow problems.
\newblock {Technical Report}, AT\&T Bell Laboratories, Holmdel, NJ~07733, USA,
  1989.

\bibitem{ipm:Rajasekera1}
J.~R. Rajasekera and S.-C. Fang.
\newblock On the convex programming approach to linear programming.
\newblock {\em Operations Research Letters}, 10:309--312, 1991.

\bibitem{ipm:Rajasekera2}
J.~R. Rajasekera and S.-C. Fang.
\newblock Deriving an unconstrained convex program for linear programming.
\newblock {\em Journal of Optimization Theory and Applications},
  75(3):603--612, 1992.

\bibitem{ipm:Ralph1}
D.~Ralph.
\newblock An affine--scaling, nonsmooth {Newton} hybrid method for constrained
  optimization.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, School of Operations Research and Industrial Engineering, Cornell
  University, Ithaca, NY~14853--3801, USA, May 1992.

\bibitem{ipm:Ralph2}
D.~Ralph and S.~J. Wright.
\newblock Superlinear convergence of an interior--point method for monotone
  variational inequalities.
\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
  Variational Problems\,: State--of--the--Art (Baltimore 1995)}, pages
  345--385. SIAM Publications, Philadelphia, PA, USA, 1997.

\bibitem{ipm:Ramakrishnan1}
K.~G. Ramakrishnan, N.~K. Karmarkar, and A.~P. Kamath.
\newblock An approximate dual projective algorithm for solving assignment
  problems.
\newblock In D.~S. Johnson and C.~C. McGeogh, editors, {\em Network Flows and
  Matching\,: First DIMACS Implementation Challenge}, volume~12 of {\em DIMACS
  Series on Discrete Mathenatics and Theoretical Computer Science}, pages
  431--451. American Mathematical Society, Providence, Rhode Island~02940, USA,
  1993.

\bibitem{ipm:Ramakrishnan2}
K.~G. Ramakrishnan, M.~G.~C. Resende, and P.~M. Pardalos.
\newblock A branch and bound algorithm for the quadratic assignment problem
  using a lower bound based on linear programming.
\newblock In C.~A. Floudas and P.~M. Pardalos, editors, {\em
  State--of--the--Art in Global Optimization\,: Computational Methods and
  Applications}, volume~7 of {\em Nonconvex Optimization and Its Applications},
  pages 57--73. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Ramana1}
M.~V. Ramana and P.~M. Pardalos.
\newblock Semidefinite programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 369--398. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Ramana2}
M.~V. Ramana, L.~Tun{\c c}el, and H.~Wolkowicz.
\newblock Strong duality for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 7:641--662, 1997.

\bibitem{ipm:Ramaswamy1}
S.~Ramaswamy and J.~E. Mitchell.
\newblock On updating the analytic center after addition of multiple cuts.
\newblock {DSES Technical Report} 37--94--423, Department of Decision Sciences
  and Engineering Systems, Rensselaer Polytechninc Institute, Troy, NY~12180,
  USA, October 1994.

\bibitem{ipm:Ramaswamy2}
S.~Ramaswamy and J.~E. Mitchell.
\newblock A long step cutting plane algorithm that uses the volumetric barrier.
\newblock {DSES Technical Report}, Department of Decision Sciences and
  Engineering Systems, Rensselaer Polytechninc Institute, Troy, NY~12180, USA,
  June 1995.

\bibitem{ipm:Rao1}
C.~V. Rao, S.~J. Wright, and J.~B. Rawling.
\newblock Application of interior--point methods to model predictive control.
\newblock {\em Journal of Optimization Theory and Applications}, 99:723--757,
  1998.

\bibitem{ipm:Rapcsak1}
T.~Rapcs{\'a}k and T.~T. Thang.
\newblock A class of polynomial variable metric algorithms for linear
  optimization.
\newblock {\em Mathematical Programming}, 74:319--331, 1996.

\bibitem{ipm:Rendl3}
F.~Rendl and C.~Helmberg.
\newblock Solving quadratic (0,\,1)--problems by semidefinite programs and
  cutting planes.
\newblock {Preprint} SC--95--35, Konrad--Zuse--Zentrum f{\"u}r
  Informationstechnik Berlin, Berlin, Germany, 1995.

\bibitem{ipm:Rendl1}
F.~Rendl, R.~J. Vanderbei, and H.~Wolkowicz.
\newblock Interior--point methods for max--min eigenvalue problems.
\newblock {Technical Report} SOR--93--15, Program in Statistics \& Operations
  Research, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, July 1993.
\newblock Also available as {\em Technical Report CORR\,93--20, Department of
  Combinatorics and Optimization, Faculty of Mathematics, University of
  Waterloo, Waterloo, Ontario, Canada}.

\bibitem{ipm:Rendl4}
F.~Rendl, R.~J. Vanderbei, and H.~Wolkowicz.
\newblock A primal--dual interior--point method for the max--min eigenvalue
  problem.
\newblock {Technical Report}, Department of Combinatorics and Optimization,
  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada,
  1993.

\bibitem{ipm:Rendl2}
F.~Rendl, R.~J. Vanderbei, and H.~Wolkowicz.
\newblock Max--min eigenvalue problems, primal--dual interior point algorithms,
  and trust region subproblems.
\newblock {\em Optimization Methods and Software}, 5:1--16, 1995.

\bibitem{ipm:Renegar2}
J.~Renegar.
\newblock Path--following methods in linear programming.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1988.

\bibitem{ipm:Renegar1}
J.~Renegar.
\newblock A polynomial--time algorithm, based on {N}ewton's method, for linear
  programming.
\newblock {\em Mathematical Programming}, 40:59--93, 1988.

\bibitem{ipm:Renegar5}
J.~Renegar.
\newblock Computational complexity of solving real algebraic formulae.
\newblock In I.~Satake, editor, {\em Proceedings of the International Congress
  of Mathematicians, Kyoto, Japan, 1990}, pages 1595--1606. Springer Verlag,
  Berlin, Germany, 1991.

\bibitem{ipm:Renegar6}
J.~Renegar.
\newblock Notes on the efficiency of the barrier method.
\newblock {Technical Report} 1039, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, January 1993.

\bibitem{ipm:Renegar7}
J.~Renegar.
\newblock Linear programming, complexity theory and elementary functional
  analysis.
\newblock {\em Mathematical Programming}, 70:279--351, 1995.

\bibitem{ipm:Renegar8}
J.~Renegar.
\newblock Condition numbers, the barrier method, and the conjugate--gradient
  method.
\newblock {\em SIAM Journal on Optimization}, 6:879--912, 1996.

\bibitem{ipm:Renegar3}
J.~Renegar and M.~Shub.
\newblock Simplified complexity analysis for {Newton LP} methods.
\newblock {Technical Report} 807, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1988.

\bibitem{ipm:Renegar4}
J.~Renegar and M.~Shub.
\newblock Unified complexity analysis for {Newton LP} methods.
\newblock {\em Mathematical Programming}, 53:1--16, 1992.

\bibitem{ipm:Resende1}
M.~G.~C. Resende.
\newblock A generalized quadratic form potential for an interior point
  algorithm for integer programming.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Mathematical Sciences Research Center, AT~\&~T~Bell Laboratories, Murray
  Hill, NJ~07974--0636, USA, July 1990.

\bibitem{ipm:Resende9}
M.~G.~C. Resende, A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock Mathematical programming approach to inductive inference.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Mathematical Sciences Research Center, AT~\&~T Bell Laboratories,
  Murray Hill, NJ~07974--0636, USA, November 1991.
\newblock See also Kamath et al. \cite{ipm:Kamath4}.

\bibitem{ipm:Resende11}
M.~G.~C. Resende, A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock An interior point approach to boolean vector function.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Mathematical Sciences Research Center, AT~\&~T Bell Laboratories,
  Murray Hill, NJ~07974--0636, USA, April 1992.
\newblock See also Kamath et al.\,\cite{ipm:Kamath5}.

\bibitem{ipm:Resende5}
M.~G.~C. Resende, N.~K. Karmarkar, A.~P. Kamath, and K.~G. Ramakrishnan.
\newblock An interior point approach to graph partitioning.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Mathematical Sciences Research Center, AT~\&~T Bell
  Laboratories, Murray Hill, NJ~07974--0636, USA, July 1991.

\bibitem{ipm:Resende19}
M.~G.~C. Resende and P.~M. Pardalos.
\newblock Interior point algorithms for network flow problems.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
  Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
  Applications}, pages 145--185. Oxford Science Publications, Oxford University
  Press, Oxford, Great Britain, 1996.
\newblock Identical to Pardalos and Resende\,\cite{ipm:Pardalos10}.

\bibitem{ipm:Resende18}
M.~G.~C. Resende, K.~G. Ramakrishnan, and Z.~Drezner.
\newblock Computing lower bounds for the quadratic assignment problem with an
  interior point algorithm for linear programming.
\newblock {\em Operations Research}, 43:781--791, 1995.

\bibitem{ipm:Resende15}
M.~G.~C. Resende, T.~Tsuchiya, and G.~Veiga.
\newblock Identifying the optimal face of a network linear program with a
  globally convergent interior point method.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 362--387.
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Resende7}
M.~G.~C. Resende and G.~Veiga.
\newblock A dual affine scaling algorithm for minimum cost network flow
  problems.
\newblock {Technical Report} 1.3, Mathematical Sciences Research Center,
  AT~\&~T Bell Laboratories, Murray Hill, NJ~07974--0636, USA, November 1990.
\newblock Revised February 1991.

\bibitem{ipm:Resende2}
M.~G.~C. Resende and G.~Veiga.
\newblock An implementation of the dual affine scaling algorithm for network
  flow problems.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Mathematical Sciences Research Center, AT~\&~T Bell Laboratories, Murray
  Hill, NJ~07974--0636, USA, July 1990.

\bibitem{ipm:Resende8}
M.~G.~C. Resende and G.~Veiga.
\newblock Computational investigation of an interior point linear programming
  algorithm for minimum cost network flow.
\newblock {Technical Report} 1.0, Mathematical Sciences Research Center,
  AT~\&~T Bell Laboratories, Murray Hill, NJ~07974--0636, USA, August 1991.

\bibitem{ipm:Resende4}
M.~G.~C. Resende and G.~Veiga.
\newblock A dual affine scaling algorithm for network flows.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Mathematical Sciences Research Center, AT~\&~T Bell
  Laboratories, Murray Hill, NJ~07974--0636, USA, July 1991.

\bibitem{ipm:Resende14}
M.~G.~C. Resende and G.~Veiga.
\newblock Computational study of two implementations of the dual affine scaling
  algorithm.
\newblock {Technical Report}, Mathematical Sciences Research Center, AT~\&~T
  Bell Laboratories, Murray Hill, NJ~07974--0636, USA, January 1992.

\bibitem{ipm:Resende12}
M.~G.~C. Resende and G.~Veiga.
\newblock An efficient implementation of a network interior point method.
\newblock {Technical Report}, Mathematical Sciences Research Center, AT~\&~T
  Bell Laboratories, Murray Hill, NJ~07974--0636, USA, February 1992.
\newblock Revised March 1992. Revised version 2.0 August 1992. See also Resende
  and Veiga \cite{ipm:Resende16}.

\bibitem{ipm:Resende10}
M.~G.~C. Resende and G.~Veiga.
\newblock Fast solution of network flow problems with a network interior point
  code.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Mathematical Sciences Research Center, AT~\&~T Bell Laboratories,
  Murray Hill, NJ~07974--0636, USA, April 1992.

\bibitem{ipm:Resende17}
M.~G.~C. Resende and G.~Veiga.
\newblock Computing the projection in an interior point algorithm\,: {An}
  experimental comparison.
\newblock {\em Investigaci{\'o}n Operativa}, 3:81--92, 1993.

\bibitem{ipm:Resende16}
M.~G.~C. Resende and G.~Veiga.
\newblock An efficient implementation of a network interior point method.
\newblock In D.~S. Johnson and C.~C. McGeogh, editors, {\em Network Flows and
  Matching\,: First DIMACS Implementation Challenge}, volume~12 of {\em DIMACS
  Series on Discrete Mathenatics and Theoretical Computer Science}, pages
  299--348. American Mathematical Society, Providence, Rhode Island~02940, USA,
  1993.
\newblock For an extended version see Resende and Veiga \cite{ipm:Resende12},
  available via NETLIB, directory netlib/att/math/resende.

\bibitem{ipm:Resende13}
M.~G.~C. Resende and G.~Veiga.
\newblock An implementation of the dual affine scaling algorithm for minimum
  cost flow on bipartite uncapacitated networks.
\newblock {\em SIAM Journal on Optimization}, 3:516--537, 1993.

\bibitem{ipm:Resende6}
M.~G.~C. Resende, G.~Veiga, and I.~Adler.
\newblock Experimentation with interior point implementations.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Mathematical Sciences Research Center, AT~\&~T Bell
  Laboratories, Murray Hill, NJ~07974--0636, USA, July 1991.

\bibitem{ipm:Resende3}
M.~G.~C. Resende and M.~H. Wright.
\newblock Sixty--six attend interior methods workshop at {A}silomar.
\newblock {\em SIAM News}, 23(3):9, May 1990.

\bibitem{ipm:Richter1}
C.~Richter.
\newblock {\em {Optimierungsverfahren und BASIC--Programme (Optimization
  Methods and BASIC--Programs)}}, chapter 2.3.2\,: {Das Projektionsverfahren
  von Karmarkar (The projection method of Karmarkar), 47--50, P.2.4.\,:
  Projektionsverfahren, BASIC--Programm}, pages 123--124.
\newblock Akademie Verlag, D--1000 Berlin, Germany, 1988.
\newblock (In German).

\bibitem{ipm:Rinaldi1}
G.~Rinaldi.
\newblock A projective method for linear programming with box--type
  constraints.
\newblock {\em Algorithmica}, 1(4):517--527, 1986.

\bibitem{ipm:Rockett1}
A.~M. Rockett and J.~C. Stevenson.
\newblock {Karmarkar's} algorithm\,: {A} method for solving large linear
  programming.
\newblock {\em BYTE}, 12(10):146--162, 1987.

\bibitem{ipm:Roehrkasse1}
R.~Roehrkasse.
\newblock Linear programming and {Operations Research}.
\newblock {\em IEEE Potentials}, 9(4):39--40, December 1990.

\bibitem{ipm:Rogers1}
J.~E. Rogers, P.~T. Boggs, and P.~D. Domich.
\newblock A predictor--corrector--{O3d} (optimal--3--dimensional) formulation
  for quadratic programming.
\newblock {Technical Report}, United States Department of Commerce, National
  Institute of Standards and Technology, Gaithersburg, MD~20899, USA, 1994.

\bibitem{ipm:Roos1}
C.~Roos.
\newblock On {Karmarkar's} projective method for linear programming.
\newblock {Technical Report} 85--23, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1985.

\bibitem{ipm:Roos15}
C.~Roos.
\newblock A pivoting rule of the simplex method which is related to
  {Karmarkar's} potential function.
\newblock {Technical Report}, Faculty of Mathematics and Informatics, TU Delft,
  NL--2628~BL~Delft, The Netherlands, 1985.

\bibitem{ipm:Roos2}
C.~Roos.
\newblock Linear programming along the trajectory of the problem.
\newblock {Technical Report} 87--41, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1987.

\bibitem{ipm:Roos4}
C.~Roos.
\newblock A new trajectory--following polynomial--time algorithm for the linear
  programming problem.
\newblock {Technical Report} 87--87, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1987.

\bibitem{ipm:Roos3}
C.~Roos.
\newblock On the trajectory of a linear programming problem.
\newblock {Technical Report} 87--53, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1987.

\bibitem{ipm:Roos6}
C.~Roos.
\newblock The influence of the potential function on the performance of a
  trajectory following algorithm for the linear programming problem.
\newblock {Technical Report} 88--44, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1988.

\bibitem{ipm:Roos5}
C.~Roos.
\newblock Linear programming along the trajectory of the problem in polynomial
  time.
\newblock {Technical Report} 88--17, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1988.

\bibitem{ipm:Roos7}
C.~Roos.
\newblock New trajectory--following polynomial--time algorithm for linear
  programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 63:433--458,
  1989.

\bibitem{ipm:Roos8}
C.~Roos.
\newblock An ${O(n^{3}L)}$ approximate center method for linear programming.
\newblock In S.~Dolecki, editor, {\em Optimization\,: Proceedings of the 5th
  French--German Conference in Castel--Novel, Varetz, France, October 1988},
  volume 1405 of {\em Lecture Notes in Mathematics}, pages 147--158. Springer
  Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Roos9}
C.~Roos.
\newblock Polynomial--time algorithms for linear programming based on the use
  of the logarithmic barrier penalty function.
\newblock {Talk held at the 14th Conference on the Mathematics of Operations
  Research in Dalfsen, The Netherlands}, Faculty of Mathematics and
  Informatics, TU Delft, NL--2628~BL~Delft, The Netherlands, January 1990.

\bibitem{ipm:Roos10}
C.~Roos.
\newblock A potential reduction method for a class of a smooth convex
  programming problem.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Faculty of
  Mathematics and Informatics, TU Delft, NL--2628~BL~Delft, The Netherlands,
  August 1990.

\bibitem{ipm:Roos16}
C.~Roos.
\newblock A projective variant of the approximate center method for linear
  programming.
\newblock {Technical Report} 90--83, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1990.

\bibitem{ipm:Roos21}
C.~Roos.
\newblock Interior point approach to linear programming\,: {Theory}, algorithms
  and parametric analysis.
\newblock In {A. H. P. van der} Burgh and J.~Simonis, editors, {\em Topics in
  Engineering\,: Modeling and Methods}, volume~81 of {\em Mathematics and Its
  Applications}, pages 181--216. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1992.
\newblock See also Jansen et al. \cite{ipm:Jansen2}.

\bibitem{ipm:Roos20}
C.~Roos.
\newblock A projective variant of the approximate center method for the dual
  linear programming problem.
\newblock In P.~Kall, editor, {\em System Modelling and Optimization
  (Proceedings of the 15th IFIP Conference, Zurich, Switzerland, September
  1991)}, volume 180 of {\em Lecture Notes in Control and Information
  Sciences}, pages 251--260. Springer Verlag, Berlin, Germany, 1992.

\bibitem{ipm:Roos18}
C.~Roos.
\newblock Interior point methods for linear programming\,: {Theory}, algorithms
  and sensitivity analysis.
\newblock In T.~F. Bewley, editor, {\em Proceedings of the Symposium on
  Engineering Mathematics}. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1995.
\newblock See also Roos \cite{ipm:Roos21}.

\bibitem{ipm:Roos11}
C.~Roos and {D. den} Hertog.
\newblock A polynomial method of approximate weighted centers for linear
  programming.
\newblock {Technical Report} 89--13, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1989.

\bibitem{ipm:Roos25}
C.~Roos and T.~Terlaky.
\newblock Advances in linear optimization.
\newblock In M.~Dell'Amico, F.~Maffioli, and S.~Martello, editors, {\em
  {Annotated Bibliography in Combinatorial Optimization}}. John Wiley \& Sons,
  New York, USA, 1997.

\bibitem{ipm:Roos24}
C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock {\em {Theory and Algorithms for Linear Optimization\,: An Interior
  Point Approach}}.
\newblock John Wiley \& Sons, New York, USA, 1997.

\bibitem{ipm:Roos26}
C.~Roos, T.~Terlaky, and J.~P. Warners.
\newblock Solving linear systems with low--rank updates.
\newblock {Technical Report} 96--149, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1996.

\bibitem{ipm:Roos13}
C.~Roos and J.-Ph. Vial.
\newblock Analytic centers in linear programming.
\newblock {Technical Report} 88--74, Faculty of Mathematics and Informatics, TU
  Delft, NL--2628~BL~Delft, The Netherlands, 1988.

\bibitem{ipm:Roos14}
C.~Roos and J.-Ph. Vial.
\newblock Long steps with the logarithmic penalty barrier function in linear
  programming.
\newblock In J.~Gabszevwicz, J.~F. Richard, and L.~A. Wolsey, editors, {\em
  Economic Decision--Making\,: Games, Economics and Optimization, dedicated to
  J. H. Dr{\`e}ze}, pages 433--441. Elsevier Science Publisher B.V., Amsterdam,
  The Netherlands, 1989.

\bibitem{ipm:Roos17}
C.~Roos and J.-Ph. Vial.
\newblock {\em Interior Point Methods for Linear Programming\,: Theory and
  Practice, Proceedings of the Symposium held in Scheveningen, The Netherlands,
  January 1990}, volume~52 of {\em Mathematical Programming}.
\newblock North Holland, Amsterdam, The Netherlands, 1991.

\bibitem{ipm:Roos12}
C.~Roos and J.-Ph. Vial.
\newblock A polynomial method of approximate centers for linear programming.
\newblock {\em Mathematical Programming}, 54:295--305, 1992.

\bibitem{ipm:Roos19}
C.~Roos and J.-Ph. Vial.
\newblock Achievable potential reductions in the method of {Kojima et al.\ } in
  the case of linear programming.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  28:135--163, 1994.

\bibitem{ipm:Roos22}
C.~Roos and J.-Ph. Vial.
\newblock Interior--point methods for linear programming.
\newblock {Technical Report} 94--77, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1994.

\bibitem{ipm:Roos23}
C.~Roos and J.-Ph. Vial.
\newblock Interior point methods.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
  Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
  Applications}, pages 47--102. Oxford Science Publications, Oxford University
  Press, Oxford, Great Britain, 1996.

\bibitem{ipm:Roth1}
G.~Roth.
\newblock {\em An ''interior point type'' algorithm for solving large scale
  nonlinear optimization problems}.
\newblock PhD thesis, Optimization Laboratory, Faculty of Industrial
  Engineering and Management, Technion--Isreal Institute of Technology, Haifa,
  Israel, 1992.

\bibitem{ipm:Rothberg2}
E.~Rothberg.
\newblock Ordering sparse matrices using approximate minimum local fill.
\newblock {Technical Report}, Silicon Graphics, Inc., Mountain View, CA~94043,
  USA, April 1996.

\bibitem{ipm:Rothberg1}
E.~Rothberg and B.~Hendrickson.
\newblock Sparse matrix ordering methods for interior point linear programming.
\newblock {\em INFORMS Journal on Computing}, 10:107--113, 1998.

\bibitem{ipm:Roubi1}
A.~Roubi.
\newblock Global convergence and rate of convergence of a method of centers.
\newblock {\em Computational Optimization and Applications}, 3:259--280, 1994.

\bibitem{ipm:Ruszczynski1}
A.~Ruszczynski.
\newblock Interior--point methods in stochastic programming.
\newblock {Technical Report} WP--93--8, International Institute for Applied
  Systems Analysis, A--2361~Laxenburg, Austria, January 1993.

\bibitem{ipm:Ruzinsky1}
S.~A. Ruzinsky and E.~T. Olsen.
\newblock ${L_1}$ and ${L_\infty}$ minimization via a variant of {Karmarkar's}
  algorithm.
\newblock {\em IEEE Transactions on Acoustics, Speech, and Signal Processing},
  37(2):245--253, 1989.

\bibitem{ipm:Saaf1}
F.~Saaf.
\newblock A user's manual for {NIPSF}\,: {Nonlinear} interior--point solver,
  {Fortran}.
\newblock {Technical Report} TR~96--24, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1996.

\bibitem{ipm:Sagara1}
N.~Sagara and M.~Fukushima.
\newblock A hybrid method for the nonlinear least squares problem with simple
  bounds.
\newblock {\em Journal of Computational and Applied Mathematics}, 36:149--157,
  1991.

\bibitem{ipm:Saigal1}
R.~Saigal.
\newblock Tracing homotopy paths in polynomial time.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Department of Industrial and Operational Engineering, University of
  Michigan, Ann Arbor, MI~48109--2117, USA, April 1988.

\bibitem{ipm:Saigal2}
R.~Saigal.
\newblock Interior point methods for the transportation problem.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Industrial and Operational Engineering, University of
  Michigan, Ann Arbor, MI~48109--2117, USA, October 1989.

\bibitem{ipm:Saigal3}
R.~Saigal.
\newblock {SOR}--type iterative techniques for interior point methods.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Industrial and Operational Engineering,
  University of Michigan, Ann Arbor, MI~48109--2117, USA, July 1991.

\bibitem{ipm:Saigal10}
R.~Saigal.
\newblock On the primal--dual affine scaling method.
\newblock {\em Journal of the Operational Research Society of India
  (Opsearch)}, 31:261--278, 1994.

\bibitem{ipm:Saigal11}
R.~Saigal.
\newblock An infeasible start predictor--corrector method for semi--definite
  linear programming.
\newblock {Technical Report}, Department of Industrial and Operational
  Engineering, University of Michigan, Ann Arbor, MI~48109--2117, USA, December
  1995.

\bibitem{ipm:Saigal4}
R.~Saigal.
\newblock An infinitely summable series implementation of interior point
  methods.
\newblock {\em Mathematics of Operations Research}, 20:597--616, 1995.

\bibitem{ipm:Saigal7}
R.~Saigal.
\newblock {\em {Linear Programming\,: A Modern Integrated Analysis}}, volume~1
  of {\em International Series in Operations Research and Management Science},
  chapter 5\,: {Interior} point methods, pp.\,111--264, chapter 6.2\,:
  {Implementation} of interior point methods, pp.\,270--305.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, November
  1995.

\bibitem{ipm:Saigal8}
R.~Saigal.
\newblock The primal power affine scaling method.
\newblock {\em Annals of Operations Research}, 62:375--417, 1996.

\bibitem{ipm:Saigal9}
R.~Saigal.
\newblock A simple proof of primal affine scaling method.
\newblock {\em Annals of Operations Research}, 62:303--324, 1996.

\bibitem{ipm:Saigal5}
R.~Saigal.
\newblock Matrix partitioning methods for interior point algorithms.
\newblock {\em Sadhana -- Academy Proceedings in Engineering Sciences},
  22:575--587, 1997.

\bibitem{ipm:Saigal6}
R.~Saigal.
\newblock A three step quadratically convergent implementation of the primal
  affine scaling method.
\newblock {\em Journal of the Operations Research Society of Japan},
  40:310--328, 1997.

\bibitem{ipm:Salamanca1}
A.~Salamanca.
\newblock An inner ellipsoid algorithm for linear programming.
\newblock {Technical Report} 1--ABR/86, Department of Mathematics, E.~T.~S. de
  Ingenieros Industriales, Universidad Politecmia de Madrid, Madrid, Spain,
  1986.

\bibitem{ipm:Albuquerque1}
J.~S.Albuquerque, V.~Gopal, G.~H. Staus, L.~T. Biegler, and B.~C. Ydstie.
\newblock Interior point {SQP} strategies for structured process optimization
  problems.
\newblock {\em Computers and Chemical Engineering}, 21:S853--S859 (Supplement),
  1997.

\bibitem{ipm:Salhi2}
A.~Salhi.
\newblock {\em Karmarkar's algorithm\,: {E}xtensions and implementations}.
\newblock PhD thesis, Department of Computer Science and Applied Mathematics,
  Aston University, Birmingham~B4~7ET, United Kingdom, 1989.

\bibitem{ipm:Salhi1}
A.~Salhi and G.~R. Lindfield.
\newblock Effects of ordering and updating techniques on the performance of the
  {Karmarkar} algorithm.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  25(2):209--236, 1991.

\bibitem{ipm:Salhi3}
A.~Salhi and G.~R. Lindfield.
\newblock Standard form {Karmarkar's} algorithm for structured linear
  programming.
\newblock In E.~F. Deprettere and A.~J. van~der Veen, editors, {\em Algorithms
  and Parallel VLSI Architectures, Vol.\,B\,: Proceedings of the International
  Workshop on Algorithms and Parallel VLSI Architectures, Pont--a--Mousson,
  France, June 1990}, pages 501--510. Elsevier Science Publishers, B.\,V.,
  Amsterdam, The Netherlands, 1991.

\bibitem{ipm:Salhi4}
A.~Salhi, G.~R. Lindfield, and L.~G. Proll.
\newblock The role of duality in the efficient use of a variant of
  {Karmarkar's} algorithm.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 516--520. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Saltzman1}
M.~J. Saltzman.
\newblock Parallel implementation of interior point {LP} algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Mathematical Sciences, Clemson University, Clemson,
  SC~29634--1907, USA, May 1990.
\newblock See Saltzman \cite{ipm:Saltzman5}.

\bibitem{ipm:Saltzman3}
M.~J. Saltzman.
\newblock {WRIP\,: A workbench for research in interior point methods}.
\newblock {Panel Discussion held at the ORSA/TIMS Joint National Meeting in
  Philadelphia, PA, USA}, Department of Mathematical Sciences, Clemson
  University, Clemson, SC~29634--1907, USA, October 1990.

\bibitem{ipm:Saltzman5}
M.~J. Saltzman.
\newblock Implementation of an interior point {LP} algorithm on a
  shared--memory vector multiprocessor.
\newblock In O.~Balci, R.~Sharda, and S.~A. Zenios, editors, {\em Operations
  Research and Computer Science: New Developments in Their Interfaces}, pages
  87--101. Pergamon Press, Oxford, United Kingdom, 1992.

\bibitem{ipm:Saltzman4}
M.~J. Saltzman and R.~Bixby.
\newblock Recovering an optimal {LP} basis from an interior point solution.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Mathematical Sciences, Clemson University, Clemson,
  SC~29634--1907, USA, April 1992.
\newblock See Bixby and Saltzman \cite{ipm:Bixby2}.

\bibitem{ipm:Saltzman2}
M.~J. Saltzman, R.~Subramaniam, and R.~E. Marsten.
\newblock Implementing an interior point {LP} algorithm on a supercomputer.
\newblock In R.~Sharda, B.~L. Golden, E.~Wasil, O.~Balci, and W.~Stewart,
  editors, {\em Impacts of Recent Computer Advances on Operations Research},
  pages 158--168. North Holland, Amsterdam, The Netherlands, 1989.

\bibitem{ipm:Samuelsen3}
C.~M. Samuelsen.
\newblock {\em The {Dikin--Karmarkar} principle for steepest descent}.
\newblock PhD thesis, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, 1992.

\bibitem{ipm:Samuelsen1}
C.~M. Samuelsen and R.~A. Tapia.
\newblock The {Dikin--Karmarkar} principle for steepest descent.
\newblock {Talk held at the Second International Conference on Industrial and
  Applied Mathematics (ICIAM~'91), Washington, DC, USA}, Department of
  Mathematical Sciences, Rice University, Houston, TX~77251, USA, July 1991.
\newblock See Samuelsen \cite{ipm:Samuelsen3}.

\bibitem{ipm:Samuelsen2}
C.~M. Samuelsen and R.~A. Tapia.
\newblock The {Dikin--Karmarkar} principle for steepest descent\,: {Avoiding}
  short steps.
\newblock {Technical Report} TR~91--20, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Sargent1}
R.~W.~H. Sargent.
\newblock A homework exercise\,--\,{The big--M problem}.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
  Optimization\,: The State--of--the--Art (Il Ciocco, Barga, Italy, September
  1993)}, volume 434 of {\em NATO ASI Series C}, pages 475--479. Kluwer
  Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Sasakawa1}
T.~Sasakawa.
\newblock A study on interior--point algorithms for linear programming.
\newblock Master's thesis, Department of Information Physics and Mathematical
  Engineering, UNiversity of Tokyo, Tokyo, Japan, 1988.
\newblock (In Japanese).

\bibitem{ipm:Saunders1}
M.~A. Saunders.
\newblock {Major Cholesky} would feel proud.
\newblock {\em ORSA Journal on Computing}, 6:23--27, 1994.

\bibitem{ipm:Saunders2}
M.~A. Saunders.
\newblock Cholesky--based methods for sparse least squares\,: {The} benefits of
  regularization.
\newblock In L.~Adams and J.~L. Nazareth, editors, {\em Linear and Nonlinear
  Conjugate Gradient--Related Methods (Proceedings of the AMS--IMS--SIAM Joint
  Summer Research Conference, Seattle, WA, USA, July 9--13, 1995)}, pages
  92--100. SIAM Publications, Philadelphia, PA, USA, 1996.

\bibitem{ipm:Schaettler1}
U.~Sch{\"a}ttler.
\newblock {\em An interior--point method for semi--infinite programming
  problems}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  1992.
\newblock See also Sch{\"a}ttler \cite{ipm:Schaettler2}.

\bibitem{ipm:Schaettler2}
U.~Sch{\"a}ttler.
\newblock An interior--point method for semi--infinite programming problems.
\newblock {\em Annals of Operations Research}, 62:277--301, 1996.
\newblock See also Sch{\"a}ttler \cite{ipm:Schaettler1}.

\bibitem{ipm:Schmieta1}
S.~Schmieta and F.~Alizadeh.
\newblock Associative algebras, symmetric cones and polynomial time interior
  point algorithms.
\newblock {RUTCOR Research Report} RRR\,17--98, RUTCOR -- Rutgers Center for
  Operations Research, Hill Center for Mathematical Sciences, New Brunswick,
  NJ~08903, USA, 1998.

\bibitem{ipm:Schneider1}
W.~Schneider.
\newblock An inner point preprocessing procedure.
\newblock {Talk held at the DGOR--Jahrestagung in Stuttgart--Hohernheim,
  Germany}, Institut f{\"u}r Informatik, Universit{\"a}t Linz, P.~O.~Box,
  A--4040~Linz, Austria, September 1991.

\bibitem{ipm:Schneider2}
W.~Schneider.
\newblock Eine innere--punkt--prozedur zur beschleunigung des
  simplexalgorithmus (an interior--point procedure for speeding up the simplex
  algorithm).
\newblock {\em Operations Research Proceedings 1991}, pages 381--388, 1992.

\bibitem{ipm:Schoenlein1}
A.~Sch{\"o}nlein.
\newblock {Der Algorithmus von Karmarkar---Idee, Realisation, Beispiel und
  numerische Erfahrungen (The Karmarkar algorithm---idea, realisation, example
  and numerical experiences)}.
\newblock {\em Angewandte Informatik}, 8:344--353, 1986.
\newblock (In German).

\bibitem{ipm:Schreck1}
H.~Schreck.
\newblock Experiences with an implementation of {Karmarkar's} {LP}--algorithm.
\newblock In M.~J. Beckmann, K.~W. Gaede, K.~Ritter, and H.~Schneeweiss,
  editors, {\em Proceedings of the X.~Symposium on Operations Research, Munich,
  Germany, August 1985}, volume~54 of {\em Methods of Operations Research},
  pages 535--542. Anton Hain Meisenheim Verlag, K{\"o}nigstein--Taunus,
  Germany, 1986.

\bibitem{ipm:Schrijver1}
A.~Schrijver.
\newblock The new linear programming method of {Karmarkar}.
\newblock {\em CWI Newsletter}, 8:2--14, 1985.

\bibitem{ipm:Schrijver2}
A.~Schrijver.
\newblock {\em Theory of Linear and Integer Programming}, chapter 15.1\,:
  {Karmarkar's} polynomial--time algorithm for linear programming, pages
  190--194.
\newblock John Wiley\,\&\,Sons, New York, 1986.

\bibitem{ipm:Schrijver3}
A.~Schrijver.
\newblock The algorithm of {N.\,K.\,Karmarkar} for linear programming.
\newblock {Talk held at the 14th Conference on the Mathematics of Operations
  Research in Dalfsen, The Netherlands}, Centre for Mathematics and Computer
  Science (CWI), Kruislaan 413, NL--1098~SJ~Amsterdam, The Netherlands, January
  1990.

\bibitem{ipm:Schultz1}
G.~L. Schultz and R.~R. Meyer.
\newblock A structured interior point method.
\newblock {Technical Report} 934, Department of Computer Science, University of
  Wisconsin, Madison, WI~53706, USA, 1990.

\bibitem{ipm:Schultz3}
G.~L. Schultz and R.~R. Meyer.
\newblock An interior point method for block angular optimization.
\newblock {\em SIAM Journal on Optimization}, 1(4):583--602, 1991.

\bibitem{ipm:Schultz2}
H.~Schultz and W.~Pulleyblank.
\newblock Trends in optimization.
\newblock {\em OR/MS Today}, 18(4):20--25, August 1991.

\bibitem{ipm:Schweitzer1}
E.~Schweitzer.
\newblock An interior random vector algorithm for multistage stochastic linear
  programs.
\newblock {\em SIAM Journal on Optimization}, 8:956--972, 1998.

\bibitem{ipm:Seifi1}
A.~Seifi and L.~Tun{\c c}el.
\newblock A constant--potential infeasible--start interior--point algorithm
  with computational experiments and applications.
\newblock {\em Computational Optimization and Applications}, 9:107--152, 1998.

\bibitem{ipm:Setiono4}
R.~Setiono.
\newblock Interior dual proximal--point algorithm using preconditioned
  conjugate gradient.
\newblock {\em Optimization}, 24:63--73, 1992.

\bibitem{ipm:Setiono2}
R.~Setiono.
\newblock Interior proximal--point algorithm for linear programs.
\newblock {\em Journal of Optimization Theory and Applications},
  74(3):425--444, 1992.

\bibitem{ipm:Setiono3}
R.~Setiono.
\newblock Interior dual least 2--norm algorithm for linear programs.
\newblock {\em Optimization}, 31:875--899, 1993.

\bibitem{ipm:Setiono1}
R.~Setiono.
\newblock Interior dual proximal--point algorithm for linear programs.
\newblock {\em European Journal of Operational Research}, 77:96--110, 1994.

\bibitem{ipm:Shanno1}
D.~F. Shanno.
\newblock Computing {Karmarkar} projections quickly.
\newblock {\em Mathematical Programming}, 41:61--71, 1988.

\bibitem{ipm:Shanno14}
D.~F. Shanno.
\newblock Current state of primal--dual interior code.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
  Mathematical Programming, Asimolar Conference Center, Pacific Grove, CA,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, March 1990.

\bibitem{ipm:Shanno3}
D.~F. Shanno.
\newblock Interior--point methods for linear programming\,: {The}
  state--of--the--art.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University, Busch
  Campus, New Brunswick, NJ~08903, USA, July 1990.

\bibitem{ipm:Shanno2}
D.~F. Shanno.
\newblock Interior--point methods for linear programming\,: {The}
  state--of--the--computational--art.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, RUTCOR\,--\,Rutgers Center of Operations Research,
  Rutgers University, Busch Campus, New Brunswick, NJ~08903, USA, January 1990.

\bibitem{ipm:Shanno12}
D.~F. Shanno.
\newblock An overview of interior point methods with implementation details and
  computational experience.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University, Busch
  Campus, New Brunswick, NJ~08903, USA, January 1991.

\bibitem{ipm:Shanno17}
D.~F. Shanno.
\newblock Computational experience with logarithmic barrier methods for linear
  and nonlinear complementarity problems.
\newblock {Research Report} RRR~18--93, RUTCOR\,--\,Rutgers Center of
  Operations Research, Rutgers University, Busch Campus, New Brunswick,
  NJ~08903, USA, 1993.

\bibitem{ipm:Shanno18}
D.~F. Shanno.
\newblock Computational methods for linear programming.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
  Optimization\,: The State--of--the--Art (Il Ciocco, Barga, Italy, September
  1993)}, volume 434 of {\em NATO Advanced Science Institute Series C\,:
  Mathematical and Physical Sciences}, pages 383--413. Kluwer Academic
  Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Shanno4}
D.~F. Shanno and A.~Bagchi.
\newblock A unified view of interior point methods for linear programming.
\newblock {\em Annals of Operations Research}, 22:55--70, 1990.

\bibitem{ipm:Shanno20}
D.~F. Shanno, M.~G. Breitfeld, and E.~M. Simantiraki.
\newblock Implementing barrier methods for nonlinear programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 399--414. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Shanno13}
D.~F. Shanno and T.~J. Carpenter.
\newblock {\em Log}--barrier methods for quadratic and linearly constrained
  nonlinear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, November 1991.

\bibitem{ipm:Shanno15}
D.~F. Shanno and T.~J. Carpenter.
\newblock Computational experience with large scale quadratic programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, April 1992.

\bibitem{ipm:Shanno16}
D.~F. Shanno and T.~J. Carpenter.
\newblock Interior point methods for large scale quadratic programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers
  University, Busch Campus, New Brunswick, NJ~08903, USA, May 1992.

\bibitem{ipm:Shanno5}
D.~F. Shanno and R.~E. Marsten.
\newblock On implementing {Karmarkar's} method.
\newblock {Working Paper} 85--01, Graduate School of Administration, University
  of California, Davis, CA~95616, USA, 1985.

\bibitem{ipm:Shanno6}
D.~F. Shanno and R.~E. Marsten.
\newblock Implementation of the {Karmarkar} algorithm within {XMP} framework.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
  FL, USA}, Graduate School of Administration, University of California, Davis,
  CA~95616, USA, October 1986.

\bibitem{ipm:Shanno7}
D.~F. Shanno and R.~E. Marsten.
\newblock A reduced--gradient variant of {Karmarkar's} algorithm and
  null--space projections.
\newblock {\em Journal of Optimization Theory and Applications}, 57:383--397,
  1988.

\bibitem{ipm:Shanno8}
D.~F. Shanno and R.~E. Marsten.
\newblock Interior point methods for linear programming\,: {Ready} for
  production use.
\newblock {Workshop held at the ORSA/TIMS Joint National Meeting in New York,
  NY, USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers
  University, Busch Campus, New Brunswick, NJ~08903, USA, October 1989.

\bibitem{ipm:Shanno9}
D.~F. Shanno and R.~E. Marsten.
\newblock Set partitioning via interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, October 1989.

\bibitem{ipm:Shanno11}
D.~F. Shanno, R.~E. Marsten, M.~J. Saltzman, and R.~Subramaniam.
\newblock Solving set partitioning problems with cutting planes and an interior
  point method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, October 1989.

\bibitem{ipm:Shanno10}
D.~F. Shanno, C.~L. Monma, and K.~McShane.
\newblock Computational experience with a primal--dual method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, April 1988.
\newblock See McShane et al.\ \cite{ipm:McShane1}.

\bibitem{ipm:Shanno19}
D.~F. Shanno and E.~M. Simantiraki.
\newblock An infeasible--interior--point method to solve the linear
  complementarity problem.
\newblock {Research Report} RRR~7--95, RUTCOR\,--\,Rutgers Center for
  Operations Research, Rutgers University, Busch Campus, New Brunswick,
  NJ~08903, USA, March 1995.

\bibitem{ipm:Shanno21}
D.~F. Shanno and E.~M. Simantiraki.
\newblock Interior point methods for linear and nonlinear programming.
\newblock In ?, editor, {\em The State--of--the--Art in Numerical Analysis},
  volume~63 of {\em Institute of Mathematics with Applications Conference
  Series (New Series)}, pages 339--362. Oxford University Press, New York, USA,
  1997.

\bibitem{ipm:Sharifi1}
F.~{Sharifi Mokhtarian} and J.-L. Goffin.
\newblock A nonlinear analytic center cutting plane method for a class of
  convex programming problems.
\newblock {\em SIAM Journal on Optimization}, 8:1108--1131, 1998.

\bibitem{ipm:Shaw6}
D.~X. Shaw.
\newblock Fractional linear functions and the analysis of variants of
  {Karmarkar's} method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, October 1989.

\bibitem{ipm:Shaw10}
D.~X. Shaw.
\newblock {\em Projective interior point methods for linear programming}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Research, Columbia University, New York, NY~10027, USA, 1991.

\bibitem{ipm:Shaw1}
D.~X. Shaw.
\newblock Several computational considerations for projective behavior point
  methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Rider College, Lawrenceville, NJ~08648, USA, April 1992.

\bibitem{ipm:Shaw3}
D.~X. Shaw.
\newblock General structures of a class of potential reduction algorithms.
\newblock {Technical Report}, School of Industrial Engineering, Purdue
  University, West Lafayette, IN\,47907, USA, August 1993.

\bibitem{ipm:Shaw5}
D.~X. Shaw.
\newblock On the complexity of a class of projective interior point methods for
  linear programming.
\newblock {Technical Report}, School of Industrial Engineering, Purdue
  University, West Lafayette, IN\,47907, USA, 1993.
\newblock See also Goldfarb and Shaw \cite{ipm:Goldfarb14}.

\bibitem{ipm:Shaw4}
D.~X. Shaw.
\newblock A self--concordant symmetric path--following algorithm for linear
  programming.
\newblock {Technical Report}, School of Industrial Engineering, Purdue
  University, West Lafayette, IN\,47907, USA, August 1993.

\bibitem{ipm:Shaw2}
D.~X. Shaw.
\newblock General structures of primal scaling interior point methods.
\newblock In A.~Bachem, U.~Derigs, M.~J{\"u}nger, and R.~Schrader, editors,
  {\em Operations Research\,'93}, pages 470--473. Physica Verlag (A
  Springer--Verlag Company), Heidelberg, Germany, 1994.
\newblock See also Shaw\,\cite{ipm:Shaw3}.

\bibitem{ipm:Shaw7}
D.~X. Shaw and D.~Goldfarb.
\newblock A primal projective interior point method for linear programming.
\newblock {Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver,
  British Columbia, Canada}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, May 1989.

\bibitem{ipm:Shaw8}
D.~X. Shaw and D.~Goldfarb.
\newblock A path--following projective interior point method for linear
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Department of Industrial Engineering and Operations Research,
  Columbia University, New York, NY~10027, USA, October 1990.

\bibitem{ipm:Shaw9}
D.~X. Shaw and D.~Goldfarb.
\newblock On the complexity of a class of projective interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, November 1991.
\newblock See Goldfarb and Shaw \cite{ipm:Goldfarb14}.

\bibitem{ipm:Sheng3}
R.~Sheng and F.~A. Potra.
\newblock Nonsymmetric search directions for semidefinite programming.
\newblock {Preprint} ANL/MCS--P692--0997, Mathematics And Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, September
  1997.

\bibitem{ipm:Sheng1}
R.~Sheng and F.~A. Potra.
\newblock A quadratically convergent infeasible--interior--point algorithm for
  {LCP} with polynomial complexity.
\newblock {\em SIAM Journal on Optimization}, 7:304--317, 1997.

\bibitem{ipm:Sheng2}
R.~Sheng, F.~A. Potra, and J.~Ji.
\newblock On a general class of interior--point algorithms for semidefinite
  programming with polynomial complexity and superlinear convergence.
\newblock {Reports on Computational Mathematics}~89, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, 1996.

\bibitem{ipm:Sherali1}
H.~D. Sherali.
\newblock Algorithmic insights and a convergence analysis for a
  {Karmarkar--type} of algorithm for linear programming problems.
\newblock {\em Naval Research Logistics Quarterly}, 34:399--416, 1987.

\bibitem{ipm:Sherali2}
H.~D. Sherali, B.~O. Skarpness, and B.~Kim.
\newblock An assumption--free convergence analysis of the scaling algorithm for
  linear programs, with application to the ${L_1}$ estimation problem.
\newblock {\em Naval Research Logistics Quarterly}, 35:473--492, 1988.

\bibitem{ipm:Sherkat1}
V.~R. Sherkat and Y.~Ikura.
\newblock Experience with interior point optimization software for a fuel
  planning application.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:833--840, 1994.
\newblock See also\,: {\em Proceedings of the Power Industry Computer
  Application Conference 1993, 89--}.

\bibitem{ipm:Sheu1}
R.-L. Sheu and S.-C. Fang.
\newblock On the relationship of interior point methods.
\newblock {Technical Report}, Operations Research Program, North Carolina State
  University, Raleigh, NC~27695, USA, November 1991.
\newblock To appear in {\em International Journal of Mathematics and
  Mathematical Sciences}.

\bibitem{ipm:Sheu2}
R.-L. Sheu and S.-C. Fang.
\newblock Insights into interior point methods.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 36(3), 1992.

\bibitem{ipm:Sheu3}
R.-L. Sheu and S.-C. Fang.
\newblock On the generalized path--following methods for linear programming.
\newblock {\em Optimization}, 30:235--249, 1994.

\bibitem{ipm:Sheu4}
R.-L. Sheu and S.-Y. Wu.
\newblock A method of weighted centers for quadratic semi--infinite programming
  with warm start.
\newblock {Technical Report}, Department of Mathematics, National Cheng--Kung
  University, Tainan, Taiwan, 1994.

\bibitem{ipm:Sheu5}
R.-L. Sheu, S.-Y. Wu, and S.-C. Fang.
\newblock A primal--dual infeasible--interior--point algorithm for linear
  semi--infinite programming.
\newblock {\em Computers and Mathematics with Applications}, 29(8):7--18, 1995.

\bibitem{ipm:Shi4}
B.~Shi and X.~Zhou.
\newblock Projected gradient type method of centers for constrained
  optimization.
\newblock {\em Journal of Mathematical Research and Exposition}, 17:375--381,
  1997.

\bibitem{ipm:Shi2}
C.-J. Shi, A.~Vannelli, and J.~Vlach.
\newblock An improvement on {Karmarkar's} algorithm for integer programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Bulletin}, 21:23--28, 1992.

\bibitem{ipm:Shi1}
M.~G. Shi.
\newblock Some convergence problems of interior point algorithms for linear
  programming.
\newblock {\em Journal of the Tsinghua University}, 28(3):91--101, 1988.
\newblock (In Chinese).

\bibitem{ipm:Shi3}
Y.~Shi.
\newblock Solving linear systems involved in constrained optimization.
\newblock {\em Linear Algebra and Its Applications}, 229:175--189, 1995.

\bibitem{ipm:Shida4}
M.~Shida.
\newblock Note on long--step predictor--corrector interior--point algorithm
  with {Monteiro--Zhang} unified search directions.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
  1004:153--167, 1997.

\bibitem{ipm:Shida3}
M.~Shida and S.~Shindoh.
\newblock Monotone semidefinite complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--312, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March 1996.

\bibitem{ipm:Shida1}
M.~Shida, S.~Shindoh, and M.~Kojima.
\newblock Centers of monotone generalized complementarity problems.
\newblock {\em Mathematics of Operations Research}, 22:969--976, 1997.

\bibitem{ipm:Shida2}
M.~Shida, S.~Shindoh, and M.~Kojima.
\newblock Existence of search directions in interior--point algorithms for the
  {SDP} and the monotone {SDLCP}.
\newblock {\em SIAM Journal on Optimization}, 8:387--396, 1998.

\bibitem{ipm:Shindoh1}
S.~Shindoh.
\newblock Semidefinite program {(SDP)}--primal--dual interior point algorithms.
\newblock {\em Journal of the Japan Society for Simulation Technology},
  16:46--52, 1997.
\newblock (In Japanese).

\bibitem{ipm:Shub1}
M.~Shub.
\newblock On the asymptotic behavior of the projective rescaling algorithm for
  linear programming.
\newblock {\em Journal of Complexity}, 3:258--269, 1987.

\bibitem{ipm:Shub2}
M.~Shub.
\newblock Boundary and asymptotic behavior of interior point methods for linear
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, IBM~T.~J.~Watson Research Center, Yorktown Heights, NY~10598, USA,
  April 1988.
\newblock See Megiddo and Shub \cite{ipm:Megiddo12}.

\bibitem{ipm:Siam1}
New algorithm stirs interest.
\newblock {\em SIAM News}, 13(1):1, 17, January 1985.

\bibitem{ipm:Sierksma1}
G.~Sierksma.
\newblock {\em Linear and Integer Programming\,: Theory and Practice}, volume
  198 of {\em Monographs and Textbooks in Pure and Applied Mathematics},
  chapter 5\,: {Karmarkar's} method for linear programming\,: {The} interior
  path version, based on Roos' lecture notes, pages 462--515.
\newblock Marcel Dekker, Inc., New York, NY, USA, 1996.

\bibitem{ipm:Silva2}
{A. de} Silva and D.~A. Abramson.
\newblock Parallel algorithms for solving stochastic linear programs.
\newblock In A.~Y. Zomaya, editor, {\em {Parallel and Distributed Computing
  Handbook}}. McGraw--Hill, New York, NY, USA, 1996.

\bibitem{ipm:Silva1}
{A. de} Silva and D.~A. Abramson.
\newblock A parallel interior point method and its application to facility
  location problems.
\newblock {\em Computational Optimization and Applications}, 9:249--273, 1998.

\bibitem{ipm:Simantiraki1}
E.~M. Simantariki and D.~F. Shanno.
\newblock An infeasible-interior-point method for solving mixed complementarity
  problems.
\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
  Variational Problems\,: State--of--the--Art (Baltimore 1995)}, pages
  386--404. SIAM Publications, Philadelphia, PA, USA, 1997.

\bibitem{ipm:Simantiraki2}
E.~M. Simantiraki and D.~F. Shanno.
\newblock An infeasible--interior--point method for linear complementarity
  problems.
\newblock {\em SIAM Journal on Optimization}, 7:620--640, 1997.

\bibitem{ipm:Singh4}
A.~Singh.
\newblock A comparison of barrier function methods with {Lagrangian} method for
  nonlinear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, University of Waterloo, Waterloo, Canada, May 1992.

\bibitem{ipm:Singh5}
A.~Singh.
\newblock A trust region method for large--scale engineering optimization using
  barrier/potential function models.
\newblock Master's thesis, University of Waterloo, Waterloo, Ontario, Canada,
  1992.

\bibitem{ipm:Singh1}
D.~Singh and J.~N. Singh.
\newblock Some remarks on {Karmarkar's} algorithm for linear programming.
\newblock {\em Journal of the Bihar Mathematical Society}, 11:85--90, 1987/88.

\bibitem{ipm:Singh7}
D.~Singh and J.~N. Singh.
\newblock Convergence in in {Karmarkar's} algorithm\,: {A} review.
\newblock {\em International Journal of Mathematical Education in Science and
  Technology}, 25:333--341, 1994.

\bibitem{ipm:Singh9}
H.~Singh and F.~L. Alvarado.
\newblock Weighted least absolute value state estimation using interior point
  methods.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:1478--1484, 1994.

\bibitem{ipm:Singh8}
J.~N. Singh.
\newblock On the completeness of {Karmarkar's} simplex.
\newblock {\em Mathematical Education}, 27(3):165--167, 1993.

\bibitem{ipm:Singh3}
J.~N. Singh, S.~Ranjan, and D.~Singh.
\newblock A modified termination rule for {Karmarkar's} algorithm.
\newblock {\em Journal of Information \& Optimization Sciences}, 16:585--591,
  1995.

\bibitem{ipm:Singh12}
J.~N. Singh and D.~Singh.
\newblock A convergence result for {Karmarkar's} algorithm for linear
  programming.
\newblock {\em Journal of the Bihar Mathematical Society}, 13:35--37, 1990.

\bibitem{ipm:Singh2}
J.~N. Singh and D.~Singh.
\newblock A modified termination rule for {Karmarkar's} algorithm.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, College of Business Management, Indian Institute of Technology,
  India, May 1992.

\bibitem{ipm:Singh6}
J.~N. Singh and D.~Singh.
\newblock A variant of {Karmarkar's} algorithm for linear programming.
\newblock {\em Journal of the Bihar Mathematical Society}, 15:21--31, 1992.

\bibitem{ipm:Singh10}
J.~N. Singh and D.~Singh.
\newblock Some remarks on {Karmarkar's} projective transformation.
\newblock {\em Acta Ciencia Indica Mathematics}, 20:271--274, 1994.

\bibitem{ipm:Singh11}
J.~N. Singh and D.~Singh.
\newblock Some remarks on {Karmarkar's} simplex and projective transformation.
\newblock {\em Acta Ciencia Indica Mathematics}, 20:297--299, 1994.

\bibitem{ipm:Singh13}
J.~N. Singh and D.~Singh.
\newblock Some remarks on the choice of step lengths in {Karmarkar's}
  algorithm.
\newblock {\em Acta Ciencia Indica Mathematics}, 21:53--58, 1995.

\bibitem{ipm:Sinha1}
L.~P. Sinha, B.~A. Freedman, N.~K. Karmarkar, A.~Puchta, and K.~G.
  Ramakrishnan.
\newblock Overseas network planning---{A}pplication of {Karmarkar's} algorithm.
\newblock In {\em Proceedings of NETWORK~'86 Conference, Tarpon Spring, FL,
  USA}, pages 8.2.1--8.2.4, June 1986.

\bibitem{ipm:Slutsman1}
L.~Slutsman.
\newblock Implementation of primal--dual series algorithm for convex separable
  quadratic programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, AT~\&~T~Bell Laboratories, Holmdel, NJ~07733, USA, October 1989.

\bibitem{ipm:Snyman2}
J.~A. Snyman.
\newblock An interior feasible direction method with constraint projections for
  linear programming.
\newblock {\em Computers and Mathematics with Applications}, 20(12):43--54,
  1990.

\bibitem{ipm:Snyman1}
J.~A. Snyman and M.~van Royen.
\newblock A multiplex algorithm for linear programming problems.
\newblock In M.~Iri and K.~Yajima, editors, {\em System Modelling and
  Optimization~ Proceedings of the 13th IFIP Conference, Tokyo, Japan,
  Aug./Sept.~1987}, volume 113 of {\em Lecture Notes in Control and Information
  Sciences}, pages 177--186. Springer Verlag, Berlin, Germany, 1988.

\bibitem{ipm:Sonnevend2}
G.~Sonnevend.
\newblock An ``analytic center'' for polyhedrons and new classes of global
  algorithms for linear (smooth, convex) programming.
\newblock In A.~Prekopa, J.~Szelezsan, and B.~Strazicky, editors, {\em System
  Modelling and Optimization\,: Proceedings of the 12th IFIP--Conference held
  in Budapest, Hungary, September 1985}, volume~84 of {\em Lecture Notes in
  Control and Information Sciences}, pages 866--876. Springer Verlag, Berlin,
  Germany, 1986.

\bibitem{ipm:Sonnevend1}
G.~Sonnevend.
\newblock A new method for solving a set of linear (convex) inequalities and
  its applications for identification and optimization.
\newblock In B.~Martos, editor, {\em Proceedings of the 5th IFAC--IFORS
  Conference held in Budapest, Hungaria, June 1986}. Pergamon Press, Oxford,
  United Kingdom, 1987.

\bibitem{ipm:Sonnevend3}
G.~Sonnevend.
\newblock New algorithms in convex programming based on a notion of ''centre''
  (for systems of analytic inequalities) and on rational extrapolation.
\newblock In K.~H. Hoffmann, J.~B. Hiriat-Urruty, C.~Lemarechal, and J.~Zowe,
  editors, {\em Trends in Mathematical Optimization\,: Proceedings of the 4th
  French--German Conference on Optimization in Irsee, Germany, April 1986},
  volume~84 of {\em International Series of Numerical Mathematics}, pages
  311--327. Birkh{\"a}user Verlag, Basel, Switzerland, 1988.

\bibitem{ipm:Sonnevend10}
G.~Sonnevend.
\newblock Application of analytic centers to feedback design for systems with
  uncertainties.
\newblock In D.~Hinrichsen and B.~Martensson, editors, {\em Control of
  Uncertain Systems}, pages 271--289. Birkh{\"a}user Verlag, Basel,
  Switzerland, 1989.

\bibitem{ipm:Sonnevend7}
G.~Sonnevend.
\newblock Applications of the notion of analytic center in approximation
  (estimation) problem.
\newblock {\em Journal of Computational and Applied Mathematics}, 28:349--358,
  1989.

\bibitem{ipm:Sonnevend4}
G.~Sonnevend.
\newblock Application of analytic centers to the design of observers and
  feedback controllers.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074 W{\"u}rzburg, Germany,
  January 1990.

\bibitem{ipm:Sonnevend8}
G.~Sonnevend.
\newblock Applications of analytic centers for the numerical solution of
  semi--infinte, convex programs arising in control theory.
\newblock In H.~J. Sebastian and K.~Tammer, editors, {\em System Modelling and
  Optimization\,: Proceedings of the 14th IFIP--Conference, Leipzig,
  East--Germany, July 1989}, volume 143 of {\em Lecture Notes in Control and
  Information Sciences}, pages 413--422. Springer Verlag, Berlin, Germany,
  1990.

\bibitem{ipm:Sonnevend11}
G.~Sonnevend.
\newblock Applications of analytic centers.
\newblock In {P. van} Dooren and G.~Golub, editors, {\em Numerical Linear
  Algebra, Digital Signal Processing and Parallel Algorithms}, volume~70 of
  {\em NATO ASI Series F\,: Computer and Systems Sciences}, pages 617--632.
  Springer Verlag, Berlin, Germany, 1991.

\bibitem{ipm:Sonnevend12}
G.~Sonnevend.
\newblock Construction and implementation of a central path following algorithm
  for semifinte convex programs in {MATLAB}.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, page 541. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Sonnevend13}
G.~Sonnevend.
\newblock A new class of a high order interior point method for the solution of
  convex semi--infinite optimization problems.
\newblock In R.~Bulirsch and D.~Kraft, editors, {\em Computational Optimal
  Control (Munich 1992)}, volume 115 of {\em International Series in Numerical
  Mathematics (ISNM)}, pages 193--211. Birkh{\"a}user Verlag, Basel,
  Switzerland, 1994.

\bibitem{ipm:Sonnevend5}
G.~Sonnevend and J.~Stoer.
\newblock Global ellipsoid approximations and homotopy methods for solving
  convex analytic programs.
\newblock {\em Applied Mathematics~\&~Optimization}, 21:139--166, 1990.

\bibitem{ipm:Sonnevend6}
G.~Sonnevend, J.~Stoer, and G.~Zhao.
\newblock On the complexity of following the central path by linear
  extrapolation in linear programming.
\newblock {\em Methods of Operations Research}, 62:19--31, 1990.

\bibitem{ipm:Sonnevend9}
G.~Sonnevend, J.~Stoer, and G.~Zhao.
\newblock On the complexity of following the central path of linear programs by
  linear extrapolation~{II}.
\newblock {\em Mathematical Programming}, 52:527--553, 1991.

\bibitem{ipm:Sonnevend14}
G.~Sonnevend, J.~Stoer, and G.~Zhao.
\newblock Subspace methods for solving linear programming problems.
\newblock {Technical Report}, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, January 1994.

\bibitem{ipm:Spedicato1}
E.~Spedicato, S.~Nicolai, and Y.~Zhao.
\newblock A faster method for computing {Karmarkar's} projections for large
  number of constraints.
\newblock {\em Optimization}, 40:343--350, 1997.

\bibitem{ipm:Spencer1}
P.~Spencer, L.~Kersley, and S.~E. Pryse.
\newblock New solution to the problem of ionosperic tomography using quadratic
  programming.
\newblock {\em Radio Science}, 33:607--616, 1998.

\bibitem{ipm:Spiegel1}
{Neuer Dampf (New power)}.
\newblock {\em Der Spiegel}, 38(49):239--240, 1984.
\newblock (In German).

\bibitem{ipm:Sridhar1}
P.~Sridhar, U.~R.~P. Kumar, and A.~K. Pujari.
\newblock Neural implementation of {Karmarkar's} algorithm.
\newblock In {\em Proceedings of the IEEE International Symposium on Circuits
  and Systems, Singapore, June 1991}, pages 1617--1620. IEEE New York, New
  York, NY, USA, 1991.

\bibitem{ipm:Steger1}
A.~E. Steger.
\newblock An extension of {Karmarkar's} algorithm for bounded linear
  programming problems.
\newblock Master's thesis, Department of Applied Mathematics, State University
  of New York, Stony Brook, NY~11794, USA, August 1985.
\newblock Condensed version in\,: H. Schellhaas, {P. van} Beek, H. Isermann, R.
  Schmidt and M. Zijlstra, editors, {\em Operations Research Proceedings 1987},
  pages 88--95, Springer Verlag, Berlin, Germany, 1988.

\bibitem{ipm:Steinbach1}
M.~C. Steinbach.
\newblock A structured interior point {SQP} method for nonlinear optimal
  control problems.
\newblock In R.~Bulirsch and D.~Kraft, editors, {\em Computational Optimal
  Control (Munich 1992)}, volume 115 of {\em International Series in Numerical
  Mathematics (ISNM)}, pages 213--222. Birkh{\"a}user Verlag, Basel,
  Switzerland, 1994.

\bibitem{ipm:Stephen1}
T.~Stephen and L.~Tun{\c{c}}el.
\newblock On a representation of the matching polytope via semidefinite
  liftings.
\newblock {Reseach Report} 97--11, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, July
  1997.

\bibitem{ipm:Stewart1}
D.~E. Stewart and S.~J. Wright.
\newblock Monotone convergent methods for a variational inequality.
\newblock {Advanced Computing Technical Report Series} 3--09--91, Australian
  National University, September 1991.

\bibitem{ipm:Stipp1}
D.~Stipp.
\newblock {AT~\&~T} problem--solving math procedure passes early tests of its
  practical value.
\newblock {\em The Wallstreet Journal}, March~5, 1985.

\bibitem{ipm:Stoer2}
J.~Stoer.
\newblock Complexity bounds for interior point methods to solve linear
  programs.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  January 1990.

\bibitem{ipm:Stoer1}
J.~Stoer.
\newblock {Innere--Punkte--Verfahren und ihre Komplexit{\"at}} {(Interior}
  point methods and their complexity).
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Institut
  f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg, Am
  Hubland, D--97074~W{\"u}rzburg, Germany, August 1990.

\bibitem{ipm:Stoer3}
J.~Stoer.
\newblock {Innere--Punkte--Verfahren zur L{\"o}sung quadratischer
  Optimierungsprobleme und ihre Komplexit{\"a}t (Interior point methods for
  solving quadratic optimization problems and their complexity)}.
\newblock In M.~Broy, editor, {\em {Informatik und Mathematik}}, pages
  137--141. Springer Verlag, Berlin, Germany, 1991.
\newblock (In German).

\bibitem{ipm:Stoer5}
J.~Stoer.
\newblock The complexity of an exterior point path--following method for the
  solution of linear programs.
\newblock {Working Paper}, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, 1992.
\newblock See also Stoer \cite{ipm:Stoer6}.

\bibitem{ipm:Stoer4}
J.~Stoer.
\newblock On interior--point methods for solving linear programs and their
  complexity.
\newblock In M.~C. Joshi, editor, {\em {Mathematical Theory of Control\,:
  Proceedings of the Mathematical Theory of Control Symposium in Bombay (India)
  1990}}, volume 142 of {\em Lecture Notes in Pure and Applied Mathematics},
  pages 337--352. Marcel Dekker, Inc., New York, USA, 1993.

\bibitem{ipm:Stoer6}
J.~Stoer.
\newblock The complexity of an infeasible interior--point path--following
  method for the solution of linear programs.
\newblock {\em Optimization Methods and Software}, 3:1--12, 1994.
\newblock See also Stoer \cite{ipm:Stoer5}.

\bibitem{ipm:Stoer7}
J.~Stoer.
\newblock Infeasible interior point methods for solving linear programs.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
  Optimization\,: The State--of--the--Art (Il Ciocco, Barga, Italy, September
  1993)}, volume 434 of {\em NATO Advanced Science Institute Series C\,:
  Mathematical and Physical Sciences}, pages 415--434. Kluwer Academic
  Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Stoer10}
J.~Stoer and M.~Wechs.
\newblock The complexity of high--order predictor--corrector methods for
  solving sufficient linear complementarity problems.
\newblock {\em Optimization Methods and Software}, 10:393--417, 1998.

\bibitem{ipm:Stoer9}
J.~Stoer and M.~Wechs.
\newblock Infeasible--interior--point paths for sufficient linear complexity
  problems and their analyticity.
\newblock {\em Mathematical Programming}, 83:407--424, 1998.

\bibitem{ipm:Stoer8}
J.~Stoer, M.~Wechs, and S.~Mizuno.
\newblock High order infeasible--interior--point methods for solving sufficient
  linear complementarity problems.
\newblock {Research Memorandum} 634, The Institute of Statistical Mathematics,
  4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, February 1997.

\bibitem{ipm:Stone2}
R.~E. Stone.
\newblock Karmarkar's algorithm.
\newblock {Unpublished Report}, Graduate School of Business Administration,
  Harvard University, Boston, MA~02163, USA, 1985.

\bibitem{ipm:Stone1}
R.~E. Stone and C.~A. Tovey.
\newblock Karmarkar's algorithm as a generalization of simplex.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
  CA, USA}, Graduate School of Business Administration, Harvard University,
  Boston, MA~02163, USA, April 1986.

\bibitem{ipm:Stone3}
R.~E. Stone and C.~A. Tovey.
\newblock The simplex and projective scaling algorithms as iteratively
  reweighted least squares methods.
\newblock {\em SIAM Review}, 33(2):220--237, June 1991.
\newblock Errata in {\em SIAM Review} 33(3):461, September 1991.

\bibitem{ipm:Stone4}
R.~E. Stone and M.~H. Wright.
\newblock Recent developments in linear and nonlinear programming.
\newblock {Short Course held at the Third SIAM Conference on Optimization in
  Boston, MA, USA}, AT\&T Bell Laboratories, Holmdel, NJ~07733, USA, April
  1989.

\bibitem{ipm:Strang1}
G.~Strang.
\newblock Karmarkar's algorithm in a nutshell.
\newblock {\em SIAM News}, 18(6):13, November 1985.

\bibitem{ipm:Strang2}
G.~Strang.
\newblock {\em Introduction to Applied Mathematics}, chapter 8.2\,: The simplex
  method and {Karmarkar's} method, pages 673--689.
\newblock Wellesley--Cambridge--Press, Cambridge, MA, USA, 1986.

\bibitem{ipm:Strang3}
G.~Strang.
\newblock Karmarkar's algorithm and its place in applied mathematics.
\newblock {\em The Mathematical Intelligencer}, 9(2):4--10, 1987.

\bibitem{ipm:Sturm5}
J.~F. Sturm.
\newblock The scaling potential reduction method.
\newblock Master's thesis, Department of Econometrics, University of Groningen,
  NL--9700~AV~Groningen, The Netherlands, 1993.

\bibitem{ipm:Sturm10}
J.~F. Sturm.
\newblock Superlinear convergence of an algorithm for monotone linear
  complementarity problems when no strictly complementary solution exists.
\newblock {Technical Report} 9596/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, The Netherlands, September 1996.

\bibitem{ipm:Sturm13}
J.~F. Sturm.
\newblock {\em Primal--dual interior point approach to semidefinite
  programming}.
\newblock PhD thesis, Tinbergen Institute, Amsterdam, The Netherlands, 1997.

\bibitem{ipm:Sturm16}
J.~F. Sturm.
\newblock Error bounds for linear matrix inequalities.
\newblock {Technical Report}, Communications Research Laboratory, McMaster
  University, 1280~Main Street West, Hamilton, Ontario~L8S\,4K1, Canada, May
  1998.

\bibitem{ipm:Sturm15}
J.~F. Sturm.
\newblock Similarity and other spectral relations for symmetric cones.
\newblock {Technical Report}, Communications Research Laboratory, McMaster
  University, 1280~Main Street West, Hamilton, Ontario~L8S\,4K1, Canada, July
  1998.

\bibitem{ipm:Sturm14}
J.~F. Sturm.
\newblock Using {SeDuMi\,1.02}, a {MATLAB} for optimization over symmetric
  cones.
\newblock {Technical Report}, Communications Research Laboratory, McMaster
  University, 1280~Main Street West, Hamilton, Ontario~L8S\,4K1, Canada, August
  1998.

\bibitem{ipm:Sturm2}
J.~F. Sturm and S.~Zhang.
\newblock A dual and interior point approach to solve convex min--max problems.
\newblock In D.-Z. Du and P.~M. Pardalos, editors, {\em Minimax and
  Applications}, volume~5 of {\em Nonconvex Optimization and Its Applications},
  pages 69--78. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995.

\bibitem{ipm:Sturm1}
J.~F. Sturm and S.~Zhang.
\newblock A potential reduction method for harmonically convex programming.
\newblock {\em Journal of Optimization Theory and Applications}, 84:181--205,
  1995.

\bibitem{ipm:Sturm7}
J.~F. Sturm and S.~Zhang.
\newblock Symmetric primal--dual path--following algorithms for semidefinite
  programming.
\newblock {Technical Report} 9554/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, The Netherlands, 1995.

\bibitem{ipm:Sturm3}
J.~F. Sturm and S.~Zhang.
\newblock New complexity results for the {Iri--Imai} method.
\newblock {\em Annals of Operations Research}, 62:539--564, 1996.

\bibitem{ipm:Sturm9}
J.~F. Sturm and S.~Zhang.
\newblock On the long--step path--following method for semidefinite
  programming.
\newblock {Technical Report}, Economic Institute, Erasmus University Rotterdam,
  NL--3000~DR~Rotterdam, The Netherlands, 1996.

\bibitem{ipm:Sturm12}
J.~F. Sturm and S.~Zhang.
\newblock On the long--step path--following method for semidefinite
  programming.
\newblock {Technical Report} 9638/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, The Netherlands, 1996.

\bibitem{ipm:Sturm11}
J.~F. Sturm and S.~Zhang.
\newblock On weighted centers for semidefinite programming.
\newblock {Technical Report} 9636/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, The Netherlands, 1996.

\bibitem{ipm:Sturm4}
J.~F. Sturm and S.~Zhang.
\newblock An $o(\sqrt{n}\,l)$ iteration bound primal--dual cone affine scaling
  algorithm for linear programming.
\newblock {\em Mathematical Programming}, 72:177--194, 1996.

\bibitem{ipm:Sturm6}
J.~F. Sturm and S.~Zhang.
\newblock On a wide region of centers and primal--dual interior point
  algorithms for linear programming.
\newblock {\em Mathematics of Operations Research}, 22:408--431, 1997.

\bibitem{ipm:Sturm8}
J.~F. Sturm and S.~Zhang.
\newblock An interior point method, based on rank--1 updates, for linear
  programming.
\newblock {\em Mathematical Programming}, 81:77--87, 1998.

\bibitem{ipm:Saunders3}
M.~Suanders and J.~A. Tomlin.
\newblock Solving regularized linear programs using barrier methods and {KKT}
  systems.
\newblock {Technical Report} SOL\,96--04, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA\,94305,
  USA, December 1996.

\bibitem{ipm:Sun1}
J.~Sun.
\newblock An affine--scaling method for linearly constrained convex programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Industrial Engineering and Management Science,
  Northwestern University, Evanston, IL~60208, USA, May 1991.

\bibitem{ipm:Sun3}
J.~Sun.
\newblock A convergence proof for an affine--scaling algorithm for convex
  quadratic programming without nondegeneracy assumptions.
\newblock {\em Mathematical Programming}, 60:69--79, 1993.

\bibitem{ipm:Sun4}
J.~Sun.
\newblock A convergence analysis for a convex version of {Dikin's} algorithm.
\newblock {\em Annals of Operations Research}, 62:357--374, 1996.

\bibitem{ipm:Sun2}
J.~Sun and L.~Qi.
\newblock An interior point algorithm of {$O(\sqrt{n} |\ln\varepsilon |)$}
  iterations for {$C^{1}$}--convex programming.
\newblock {\em Mathematical Programming}, 57:239--257, 1992.

\bibitem{ipm:Sun11}
J.~Sun, K.-E. Wee, and J.~Zhu.
\newblock An interior point method for solving a class of linear--quadratic
  stochastic programming problems.
\newblock In D.-Z. Du, L.~Qi, and R.~S. Womersley, editors, {\em Recent
  Advances in Nonsmooth Optimization}, pages 392--404. World Scientific
  Publishing Co., River Edge, NJ~07661, USA, 1995.

\bibitem{ipm:Sun10}
J.~Sun and G.~Zhao.
\newblock A quadratically convergent long--step interior--point method for
  nonlinear monotone variational inequality problems.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, April 1996.

\bibitem{ipm:Sun8}
J.~Sun and G.~Zhao.
\newblock Global linear and local quadratic convergence of a long--step
  adaptive--mode interior point method for some monotone variational inequality
  problems.
\newblock {\em SIAM Journal on Optimization}, 8:123--139, 1998.

\bibitem{ipm:Sun9}
J.~Sun and J.~Zhu.
\newblock A predictor--corrector method for extended linear--quadratic
  programming.
\newblock {\em Computers and Operations Research}, 23:755--767, 1996.

\bibitem{ipm:Sun6}
J.~Sun, J.~Zhu, and W.~K. Eng.
\newblock Computational experiments on {ELQP} problems using interior point
  methods.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, 1995.

\bibitem{ipm:Sun7}
J.~Sun, J.~Zhu, and G.~Zhao.
\newblock A quadratically convergent polynomial long--step algorithm for a
  class of nonlinear monotone complementarity problems.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, January 1996.

\bibitem{ipm:Sun5}
J.~Sun, J.~Zhu, and G.~Zhao.
\newblock A predictor--corrector algorithm for a class of nonlinear saddle
  point problems.
\newblock {\em SIAM Journal on Control and Optimization}, 35:532--551, 1997.

\bibitem{ipm:Swart1}
E.~R. Swart.
\newblock How {I} implemented the {Karmarkar} algorithm in one evening.
\newblock {\em APL Quote Quad}, 15(3):13--16, 1985.

\bibitem{ipm:Swart2}
E.~R. Swart.
\newblock A modified version of the {Karmarkar} algorithm.
\newblock {Research Report in Mathematics}~98, Department of Mathematics and
  Statistics, University of Guelph, Guelph, Ontario~N1G~2W1, Canada, 1985.

\bibitem{ipm:Szymanski1}
P.~T. Szymanski and M.~D. Lemmon.
\newblock Interior point methods in the design of hierarchical controllers.
\newblock {\em Proceedings of the 1994 IEEE International Symposium on
  Intelligent Control (Columbus, Ohio, USA, August 1994)}, pages 33--38, 1994.

\bibitem{ipm:Tachat1}
D.~Tachat.
\newblock {\em Methodes interieures en programmation lineaire\,: {Elaboration}
  et mise en oeuvre de procedures de projection exacte et approchee {(Interior
  point methods for linear programming\,: Computing exact and approximate
  projections)}}.
\newblock PhD thesis, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1991.
\newblock (In French).

\bibitem{ipm:Takehara1}
H.~Takehara.
\newblock An interior point algorithm for large scale portfolio optimization.
\newblock {\em Annals of Operations Research}, 45:373--386, 1993.

\bibitem{ipm:Tamiz1}
M.~Tamiz.
\newblock {\em Design, implementation and testing a general linear programming
  system exploiting sparsity}.
\newblock PhD thesis, Department of Mathematics and Statistics, Brunel
  University, Uxbridge, Middlesex~UB8\,3PH, United Kingdom, 1986.

\bibitem{ipm:Tamura1}
A.~Tamura, H.~Takehara, K.~Fukuda, S.~Fujishige, and M.~Kojima.
\newblock A dual interior primal simplex method for linear programming.
\newblock {\em Journal of the Operations Research Society of Japan},
  31:413--429, 1988.

\bibitem{ipm:Tamura2}
T.~E. Tamura.
\newblock Characteristics of {Karmarkar} method compared with simplex method.
\newblock {\em Bulletin of Nagoya Institute of Technology (Nagoya, Japan)},
  38:251--256, 1986.
\newblock (In Japanese).

\bibitem{ipm:Tan1}
K.~C. Tan and R.~M. Freund.
\newblock Newton's method for general parametric center problem with
  applications.
\newblock {Technical Report} RR~457, Department of Mathematics, National
  University of Singapore, Singapore~0511, 1991.

\bibitem{ipm:Tanabe4}
K.~Tanabe.
\newblock Center flattening transformation and a centered {N}ewton method for
  linear programming.
\newblock {Technical Report}, The Institute of Statistical Mathematics,
  4--6--7~Minami Azabu, Minatoku, Tokyo~106, Japan, 1987.

\bibitem{ipm:Tanabe6}
K.~Tanabe.
\newblock Centered {Newton} method for liner programming and quadratic
  programming.
\newblock {\em Proceedings of the 8th Mathematical Programming Symposium in
  Japan}, pages 131--152, 1987.

\bibitem{ipm:Tanabe1}
K.~Tanabe.
\newblock Complementarity--enforced centered {N}ewton method for mathematical
  programming.
\newblock In K.~Tone, editor, {\em New Methods for Linear Programming}, pages
  118--144, The Institute of Statistical Mathematics, 4--6--7~Minami Azabu,
  Minatoku, Tokyo~106, Japan, 1987.

\bibitem{ipm:Tanabe2}
K.~Tanabe.
\newblock Centered {Newton} method for mathematical programming.
\newblock In M.~Iri and K.~Yajima, editors, {\em System Modelling and
  Optimization\,: Proceedings of the 13th IFIP Conference, Tokyo, Japan,
  Aug./Sept.~1987}, volume 113 of {\em Lecture Notes in Control and Information
  Sciences}, pages 197--206. Springer Verlag, Berlin, Germany, 1988.

\bibitem{ipm:Tanabe3}
K.~Tanabe.
\newblock Centered {N}ewton method for linear programming exterior point
  method.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, The Institute of Statistical Mathematics, 4--6--7~Minami Azabu,
  Minatoku, Tokyo~106, Japan, January 1990.

\bibitem{ipm:Tanabe7}
K.~Tanabe.
\newblock Centered {Newton} method for linear programming\,: {Interior} and
  {''exterior''} point method.
\newblock In K.~Tone, editor, {\em New Methods for Linear Programming~3}, pages
  98--100. Institute of Statistical Mathematics, Tokyo, Japan, 1990.
\newblock In Japanese.

\bibitem{ipm:Tanabe8}
K.~Tanabe.
\newblock Center {Newton} methods and differential geometry of optimization.
\newblock {Cooperative Research Report}~89, The Institute of Statistical
  Mathematics, 4--6--7~Minami Azabu, Minatoku, Tokyo~106, Japan, 1996.
\newblock Contains 38 references related to the subject.

\bibitem{ipm:Tanabe5}
K.~Tanabe and T.~Tsuchiya.
\newblock Global analysis of dynamical systems associated with {Karmarkar's}
  method for linear programming.
\newblock {\em Proceedings of the Annual Meeting of the Operations Research
  Society of Japan}, pages 132--133, 1987.

\bibitem{ipm:Tang1}
H.-W. Tang and G.-B. Li.
\newblock Karmarkar's algorithm and fractional linear programming.
\newblock {\em Journal of the Dalian Institute of Technology}, 25:79--83
  (suppl.), 1986.
\newblock (In Chinese).

\bibitem{ipm:Tapia1}
R.~A. Tapia.
\newblock Current research in numerical optimization.
\newblock {\em SIAM News}, 20:10--11, March 1987.

\bibitem{ipm:Tapia2}
R.~A. Tapia.
\newblock Accelerating interior--point methods.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, January 1990.

\bibitem{ipm:Tapia12}
R.~A. Tapia.
\newblock On the fundamental role of interior--point methodology in constrained
  optimization.
\newblock {Technical Report} TR~97--06, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1997.

\bibitem{ipm:Tapia3}
R.~A. Tapia and Y.~Zhang.
\newblock An optimal basis identification technique for interior point linear
  programming methods.
\newblock {Technical Report} TR--89--01, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, April 1989.
\newblock Revised September 1990. Essentially contained in Tapia and Zhang
  \cite{ipm:Tapia7}.

\bibitem{ipm:Tapia4}
R.~A. Tapia and Y.~Zhang.
\newblock Accelerating the convergence of interior point methods.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Department of Mathematical Sciences, Rice University, Houston, TX~77251, USA,
  July 1990.

\bibitem{ipm:Tapia5}
R.~A. Tapia and Y.~Zhang.
\newblock A cubically convergent method for locating a nearby vertex in linear
  programming.
\newblock {\em Journal of Optimization Theory and Applications}, 67:217--225,
  1990.

\bibitem{ipm:Tapia7}
R.~A. Tapia and Y.~Zhang.
\newblock An optimal--basis identification technique for interior--point linear
  programming algorithms.
\newblock {\em Linear Algebra and Its Applications}, 152:343--363, 1991.

\bibitem{ipm:Tapia6}
R.~A. Tapia and Y.~Zhang.
\newblock A polynomial and superlinearly convergent primal--dual interior
  algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, May 1991.

\bibitem{ipm:Tapia10}
R.~A. Tapia and Y.~Zhang.
\newblock Interpretation and optimality properties of the {Karmarkar}
  algorithm.
\newblock {Technical Report} (in preparation), Department of Mathematical
  Sciences, Rice University, Houston, TX~77251, USA, 1992.

\bibitem{ipm:Tapia11}
R.~A. Tapia and Y.~Zhang.
\newblock On the quadratic convergence of the singular {Newton's} method.
\newblock {\em SIAG/OPT Views--and--News, A forum for the SIAM Activity Group
  on Optimization}, 1:6--8, 1992.

\bibitem{ipm:Tapia8}
R.~A. Tapia, Y.~Zhang, M.~Saltzman, and A.~Weiser.
\newblock The {Mehrotra} predictor--corrector interior--point method as a
  perturbed composite {Newton} method.
\newblock {\em SIAM Journal on Optimization}, 6:47--56, 1996.

\bibitem{ipm:Tapia9}
R.~A. Tapia, Y.~Zhang, and Y.~Ye.
\newblock On the convergence of the iteration sequence in primal--dual interior
  point methods.
\newblock {\em Mathematical Programming}, 68:141--154, 1995.

\bibitem{ipm:Tarasov1}
S.~P. Tarasov, L.~G. Khachiyan, and I.~I. Erlikh.
\newblock The method of inscribed ellipsoids.
\newblock {\em Soviet Mathematics Doklady}, 37:226--230, 1988.

\bibitem{:Terlaky1}
T.~Terlaky.
\newblock A {Karmarkar} tipusu algoritmusokrol ({On Karmarkar} type
  algorithms).
\newblock {\em Alkalmazott Matematikai Lapok}, 15:133--162, 1990/91.
\newblock (In Hungarian, English summary).

\bibitem{ipm:Terlaky2}
T.~Terlaky.
\newblock {\em {Interior Point Algorithms of Mathematical Programming}},
  volume~5 of {\em Applied Optimization}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Terlaky5}
T.~Terlaky.
\newblock An easy way to teach interior--point methods.
\newblock {Technical Report} 98--24, Faculty of Information Technology and
  Systems Subfaculty of Technical Mathematics and Informatics, Department of
  Statistics, Stochastic and Operations Research Delft University of
  Technology, P.O.\,Box\,5031, NL--2600~GA~Delft, The Netherlands, 1998.

\bibitem{ipm:Terlaky4}
T.~Terlaky and T.~Tsuchiya.
\newblock A note on {Mascarenhas'} counter example about global convergence of
  the affine scaling algorithm.
\newblock {Research Memorandum} 596, The Institute of Statistical Mathematics,
  4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, March 1996.

\bibitem{ipm:Terlaky3}
T.~Terlaky and J.-Ph. Vial.
\newblock Computing maximum likelihood estimators of convex density functions.
\newblock {Technical Report} 95--49, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Thompson1}
R.~G. Thompson, P.~S. Dharmapala, J.~B. Diaz, M.~D. Gonzalez-Lima, and R.~M.
  Thrall.
\newblock {DEA} multiplier analytic center sensitivity with an illustrative
  application to independent oil companies.
\newblock {\em Annals of Operations Research}, 66:163--177, 1996.

\bibitem{ipm:Thys1}
R.~Thys and {C. van} Nuffelen.
\newblock An implementation of {Karmarkar's} interior point algorithm.
\newblock {Working Paper} 89--124, Department of Economics and Econometrics,
  University of Antwerpen, Antwerpen, Belgium, 1989.

\bibitem{ipm:Tits1}
A.~L. Tits and J.~L. Zhou.
\newblock A simple, quadratically convergent interior point algorithm for
  linear programming and convex quadratic programming.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 411--427.
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Todd1}
M.~J. Todd.
\newblock A review of {N. Karmarkar}.
\newblock {\em Computing Reviews}, 27:95--96, March 1986.

\bibitem{ipm:Todd6}
M.~J. Todd.
\newblock The effects of degeneracy and sparsity on {Karmarkar's} projective
  algorithm and its variants.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1988.
\newblock See Todd \cite{ipm:Todd9}.

\bibitem{ipm:Todd4}
M.~J. Todd.
\newblock Exploiting special structure in {Karmarkar's} algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 41:97--113, 1988.

\bibitem{ipm:Todd3}
M.~J. Todd.
\newblock Improved bounds and containing ellipsoids in {Karmarkar's} linear
  programming algorithm.
\newblock {\em Mathematics of Operations Research}, 13:650--659, 1988.

\bibitem{ipm:Todd2}
M.~J. Todd.
\newblock Polynomial algorithms for linear programming.
\newblock In H.~A. Eiselt, editor, {\em Advances in Optimization and Control,
  Proceedings of the Conference {''Optimization Days '86''} held at Montreal,
  Quebec, Canada, April/May 1986}, volume 302 of {\em Lecture Notes in
  Economics and Mathematical Systems}, pages 49--66. Springer Verlag, Berlin,
  Germany, 1988.

\bibitem{ipm:Todd11}
M.~J. Todd.
\newblock Anticipated behavior of {Karmarkar's} algorithm.
\newblock {Technical Report} 879, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, December 1989.

\bibitem{ipm:Todd7}
M.~J. Todd.
\newblock Recent developments and new directions in linear programming.
\newblock In M.~Iri and K.~Tanabe, editors, {\em Mathematical Programming\,:
  Recent Developments and Applications}, pages 109--157. Kluwer Academic Press,
  Dordrecht, The Netherlands, 1989.

\bibitem{ipm:Todd12}
M.~J. Todd.
\newblock Anticipated behavior of interior point methods for linear
  programming.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, January 1990.
\newblock See Todd \cite{ipm:Todd11}, Mizuno et al.\,%
  \cite{ipm:Mizuno4,ipm:Mizuno5}.

\bibitem{ipm:Todd5}
M.~J. Todd.
\newblock A {Dantzig--Wolfe--like variant of Karmarkar's} interior--point
  linear programming algorithm.
\newblock {\em Operations Research}, 38:1006--1018, 1990.

\bibitem{ipm:Todd9}
M.~J. Todd.
\newblock The effects of degeneracy, null and unbounded variables on variants
  of {Karmarkar's} linear programming algorithm.
\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
  Optimization, Papers from the Workshop held at Cornell University, Ithaca,
  NY, USA, October 1989}, volume~46 of {\em SIAM Proceedings in Applied
  Mathematics}, pages 81--91. Society of Industrial and Applied Mathematics
  (SIAM), Philadelphia, PA, USA, 1990.

\bibitem{ipm:Todd18}
M.~J. Todd.
\newblock Projected scaled steepest descent in {Kojima--Mizuno--Yoshise's}
  potential reduction algorithm for the linear complementarity problem.
\newblock {Technical Report} 950, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, December 1990.

\bibitem{ipm:Todd10}
M.~J. Todd.
\newblock The affine--scaling direction for linear programming is a limit of
  projective--scaling directions.
\newblock {\em Linear Algebra and Its Applications}, 152:93--105, 1991.

\bibitem{ipm:Todd26}
M.~J. Todd.
\newblock Another derivation of the {Karmarkar} direction for linear
  programming.
\newblock {Technical Report} 91--20, Computational Optimization Project, Center
  for Applied Mathematics, Cornell University, Ithaca, NY~14853--3801, USA,
  December 1991.

\bibitem{ipm:Todd22}
M.~J. Todd.
\newblock Playing with interior points.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:17--25, August 1991.

\bibitem{ipm:Todd24}
M.~J. Todd.
\newblock Probabilistic models in linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):671--693, 1991.

\bibitem{ipm:Todd13}
M.~J. Todd.
\newblock A low complexity interior point algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:198--209, 1992.

\bibitem{ipm:Todd8}
M.~J. Todd.
\newblock On {Anstreicher's} combined {phase\,I\,--\,phase\,II} projective
  algorithm for linear programming.
\newblock {\em Mathematical Programming}, 55:1--15, 1992.

\bibitem{ipm:Todd25}
M.~J. Todd.
\newblock Recent developments on interior point methods for linear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, School of Operations Research and Industrial Engineering, Cornell
  University, Ithaca, NY~14853--3801, USA, May 1992.
\newblock There is no underlying report.

\bibitem{ipm:Todd19}
M.~J. Todd.
\newblock Combining {phase\,I and phase\,II} in a potential reduction algorithm
  for linear programming.
\newblock {\em Mathematical Programming}, 59:133--150, 1993.

\bibitem{ipm:Todd29}
M.~J. Todd.
\newblock A lower bound on the number of iterations of primal--dual
  interior--point methods for linear programming.
\newblock {Technical Report} 1050, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, March 1993.
\newblock Revised June 1993.

\bibitem{ipm:Todd28}
M.~J. Todd.
\newblock Analysis of interior--point methods for linear programming problems
  with variable upper bounds.
\newblock In S.~Gomez and J.~P. Hennart, editors, {\em Advances in Optimization
  and Numerical Analysis (Proceedings of the Sixth Workshop on Optimization and
  Numerical Analysis, Oaxaca, Mexico, 1992)}, volume 275 of {\em Mathematics
  and Its Applications}, pages 1--23. Kluwer Academic Publishers, Dordrecht,
  The Netherlands, 1994.

\bibitem{ipm:Todd27}
M.~J. Todd.
\newblock Interior--point algorithms for semi--infinite programming.
\newblock {\em Mathematical Programming}, 65:217--245, 1994.

\bibitem{ipm:Todd31}
M.~J. Todd.
\newblock On lower bound on the number of iteration of an interior--point
  algorithm for linear programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
  1993}, volume 303 of {\em Pitman Research Notes in Mathematics}, pages
  237--259. Longman Scientific \& Technical, Harlow, United Kingdom, 1994.
\newblock See also Todd and Ye \cite{ipm:Todd33}.

\bibitem{ipm:Todd32}
M.~J. Todd.
\newblock Scaling, shifting and weighting in interior--point methods.
\newblock {\em Computational Optimization and Applications}, 3:305--315, 1994.

\bibitem{ipm:Todd30}
M.~J. Todd.
\newblock Theory and practice for interior--point methods.
\newblock {\em ORSA Journal on Computing}, 6:28--31, 1994.

\bibitem{ipm:Todd38}
M.~J. Todd.
\newblock On adjusting parameters in homotopy methods for linear programming.
\newblock In {\em Approximation Theory and Optimization}, pages 201--220.
  Cambridge University Press, Cambridge, UK, 1997.

\bibitem{ipm:Todd39}
M.~J. Todd.
\newblock On search directions in interior--point methods for semidefinite
  programming.
\newblock {Technical Report} 1205, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, October 1997.

\bibitem{ipm:Todd36}
M.~J. Todd.
\newblock Potential--reduction methods in mathematical programming.
\newblock {\em Mathematical Programming}, 76:3--45, 1997.

\bibitem{ipm:Todd40}
M.~J. Todd.
\newblock A short history of interior--point methods.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1998.

\bibitem{ipm:Todd14}
M.~J. Todd and B.~P. Burrell.
\newblock An extension of {Karmarkar's} algorithm for linear programming using
  dual variables.
\newblock {\em Algorithmica}, 1(4):409--424, 1986.

\bibitem{ipm:Todd15}
M.~J. Todd and C.~C. Gonzaga.
\newblock An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine
  algorithm for linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, School of Operations Research and Industrial Engineering,
  Cornell University, Ithaca, NY~14853--3801, USA, January 1990.
\newblock See Gonzaga and Todd \cite{ipm:Gonzaga12}.

\bibitem{ipm:Todd34}
M.~J. Todd and S.~Herzel.
\newblock Interior point algorithms for a class of convex programming problems.
\newblock {Technical Report} 1097, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, June 1994.

\bibitem{ipm:Todd23}
M.~J. Todd, S.~Mizuno, and Y.~Ye.
\newblock Anticipated behavior of path--following algorithms for linear
  programming.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
  Mathematical Programming, Asilomar, CA, USA}, School of Operations Research
  and Industrial Engineering, Cornell University, Ithaca, NY~14853--3801, USA,
  February 1990.
\newblock See Mizuno et al.\ \cite{ipm:Mizuno4}.

\bibitem{ipm:Todd37}
M.~J. Todd, K.~Toh, and R.~T{\"u}t{\"u}nc{\"u}.
\newblock On the {Nesterov--Todd} direction in semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:769--796, 1998.

\bibitem{ipm:Todd41}
M.~J. Todd, L.~Tun{\c c}el, and Y.~Ye.
\newblock Probabilistic analysis of two complexity measures for linear
  programming problems.
\newblock {Technical Report} TR~1219, School of Operations Research and
  Industrial Engineering, Cornell University, Ithaca, NY~14853--3801, USA,
  October 1998.
\newblock Also available as {\it{CORR 98--48, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario, Canada, October
  1998}}.

\bibitem{ipm:Todd20}
M.~J. Todd and J.-Ph. Vial.
\newblock Todd's low--complexity algorithm is a predictor--corrector
  path--following method.
\newblock {\em Operations Research Letters}, 11:199--207, 1992.

\bibitem{ipm:Todd21}
M.~J. Todd and Y.~Wang.
\newblock A projective algorithm for convex quadratic programming.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1991.

\bibitem{ipm:Todd16}
M.~J. Todd and Y.~Wang.
\newblock On combined {phase\,I\,--\,phase\,II} projective methods for linear
  programming.
\newblock {\em Algorithmica}, 9(1):64--83, 1993.

\bibitem{ipm:Todd17}
M.~J. Todd and Y.~Ye.
\newblock A centered projective algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 15:508--529, 1990.

\bibitem{ipm:Todd33}
M.~J. Todd and Y.~Ye.
\newblock A lower bound on the number of iterations of long--step primal--dual
  linear programming algorithms.
\newblock {\em Annals of Operations Research}, 62:233--252, 1996.

\bibitem{ipm:Todd35}
M.~J. Todd and Y.~Ye.
\newblock Approximate {Farkas Lemmas} and stopping rules for iterative
  infeasible--point algorithms for linear programming.
\newblock {\em Mathematical Programming}, 81:1--21, 1998.

\bibitem{ipm:Toh2}
K.~C. Toh.
\newblock Search directions for primal--dual interior point methods in
  semidefinite programming.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, July 1997.

\bibitem{ipm:Toh1}
K.~C. Toh, M.~J. Todd, and R.~H. T{\"u}t{\"u}nc{\"u}.
\newblock {SDPT3 -- A MATLAB software package for semidefinite programming}.
\newblock {Manuscript}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1996.

\bibitem{ipm:Tolla2}
P.~Tolla.
\newblock Amelioration des performances de l'algorithme de {Karmarkar} dans le
  cas de programmes lineaires a variables bornees superieurement {(Improvment
  of the efficiency of {Karmarkar's algorithm} for linear programs with upper
  bounded variables)}.
\newblock Cahier~82, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, November 1987.
\newblock (In French).

\bibitem{ipm:Tolla1}
P.~Tolla.
\newblock Validation numerique de l'algorithme de {Karmarkar} {(Numerical
  validation of Karmarkar's algorithm)}.
\newblock Cahier~76, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, April 1987.
\newblock (In French).

\bibitem{ipm:Tolla6}
P.~Tolla.
\newblock New numerical results on {Karmarkar's} algorithm.
\newblock Cahier, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1988.

\bibitem{ipm:Tolla4}
P.~Tolla.
\newblock Elaboration de logiciels efficaces utilisant l'algorithme de
  {Karmarkar} {(Elaboration of a computationally efficient utilization of
  Karmarkar's algorithm)}.
\newblock In J.~P. Penot, editor, {\em New Methods in Optimization and Their
  Industrial Uses}, volume~87 of {\em International Series of Numerical
  Mathematics}, pages 173--190. Birkh{\"a}user Verlag, Basel, Switzerland,
  1989.
\newblock (In French).

\bibitem{ipm:Tolla3}
P.~Tolla.
\newblock Optimal termination criterion and optimal solution accuracy test in
  the {Karmarkar's} algorithm.
\newblock In C.~Brezinski, editor, {\em Numerical and Applied Mathematics,
  Part~II. Papers from the Twelfth IMACS World Congress on Scientific
  Computation in Paris, France, July 1988}, volume 1.2 of {\em IMACS Annals of
  Computational and Applied Mathematics}, pages 629--633. Baltzer Verlag,
  Basel, Switzerland, 1989.

\bibitem{ipm:Tolla5}
P.~Tolla.
\newblock Implementation and validation of interior point methods for linear
  programming.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, July 1991.

\bibitem{ipm:Tomlin1}
J.~A. Tomlin.
\newblock Experimental results with an implementation of the projective method.
\newblock Early draft of Tomlin \cite{ipm:Tomlin2}, 1985.

\bibitem{ipm:Tomlin2}
J.~A. Tomlin.
\newblock An experimental approach to {Karmarkar's} projective method for
  linear programming.
\newblock {\em Mathematical Programming Study}, 31:175--191, 1987.

\bibitem{ipm:Tomlin3}
J.~A. Tomlin.
\newblock A note on comparing simplex and interior methods for linear
  programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 91--104. Springer Verlag, New
  York, 1989.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tomlin6}
J.~A. Tomlin and J.~J. Forrest.
\newblock Switching from interior to vertex solutions in {OSL (Optimization
  Subroutine Library)}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, IBM Almaden Research Center, San Jose, CA~95120, USA, April 1992.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tomlin4}
J.~A. Tomlin and J.~S. Welch.
\newblock Implementing an interior point method in a mathematical programming
  system\,: {Part\,I}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami, FL,
  USA}, Ketron Management Science, Inc., Mountain View, CA~94040, USA, October
  1986.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tomlin5}
J.~A. Tomlin and J.~S. Welch.
\newblock Implementing an interior point method in a mathematical programming
  system.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New Orleans,
  USA}, Ketron Management Science, Inc., Mountain View, CA~94040, USA, May
  1987.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}, and Tomlin
  \cite{ipm:Tomlin3}.

\bibitem{ipm:Tomlin7}
J.~A. Tomlin and J.~S. Welsch.
\newblock {Mathematical Programming Systems}.
\newblock In E.~G. {Coffman, Jr.}, J.~K. Lenstra, and A.~H.~G. {Rinnooy Kan},
  editors, {\em Computing}, volume~3 of {\em Handbooks in Operations Research
  and Management Science}, pages 561--601. North Holland, Amsterdam, The
  Netherlands, 1992.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tompkins1}
C.~B. Tompkins.
\newblock Projection methods in calculation.
\newblock In H.~A. Antosiewicz, editor, {\em Proceedings of the Second
  Symposium in Linear Programming}, pages 425--448, U.~S.~Air Force,
  Washington, DC, USA, 1955.

\bibitem{ipm:Tompkins2}
C.~B. Tompkins.
\newblock Some methods of computational attack on programming problems, other
  than the simplex method.
\newblock {\em Naval Research Logistics Quarterly}, 4:95--96, 1957.

\bibitem{ipm:Tone1}
K.~Tone.
\newblock A hybrid method for linear programming.
\newblock {Technical Report} 85--B--1, Graduate School for Policy Science,
  Saitama University, Urawa, Saitama~338, Japan, 1985.

\bibitem{ipm:Tone2}
K.~Tone.
\newblock An implementation of a revised {Karmarkar} method.
\newblock {Technical Report}, Graduate School for Policy Science, Saitama
  University, Urawa, Saitama~338, Japan, 1986/87.

\bibitem{ipm:Tone4}
K.~Tone.
\newblock An {$O(\sqrt{n}L)$} iteration large--step logarithmic barrier
  function algorithm for linear programming.
\newblock {Research Report} 89--B--5, Graduate School for Policy Science,
  Saitama University, Urawa, Saitama~338, Japan, 1989.

\bibitem{ipm:Tone3}
K.~Tone.
\newblock Linear programming and {Karmarkar} patents.
\newblock {\em Systems, Control and Information}, 34(5):209--215, April 1990.
\newblock (In Japanese).

\bibitem{ipm:Tone6}
K.~Tone.
\newblock Remarks on potential versus barrier function methods for linear
  programming.
\newblock {\em Journal of the Operations Research Society of Japan},
  34(4):436--448, 1991.

\bibitem{ipm:Tone5}
K.~Tone.
\newblock An active--set strategy in interior point method for linear
  programming.
\newblock {\em Mathematical Programming}, 59:345--360, 1993.

\bibitem{ipm:Torabi1}
M.~Torabi.
\newblock Decomposed block {Cholesky} factorization in the {Karmarkar}
  algorithm\,: {A} proposed scheme for solving a class of super large {LP}
  problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA, May 1990.

\bibitem{ipm:Torabi2}
M.~Torabi.
\newblock Decomposed block {Cholesky} factorization in the {Karmarkar}
  algorithm.~{S}olving a class of super large {LP} problems.
\newblock {\em Computers and Mathematics with Applications}, 20(2):1--7, 1990.

\bibitem{ipm:Torres1}
G.~L. Torres and V.~H. Quintana.
\newblock Optimal power flow via interior point methods\,: {An} educational
  tool in {MATLAB}.
\newblock {\em Proceedings of the 1996 Canadian Conference on Electrical and
  Computer Engineering}, 2/2:996--999, 1996.

\bibitem{ipm:Tovey1}
C.~A. Tovey.
\newblock Integrating {Karmarkar's} algorithm into the curriculum.
\newblock {Workshop held at the ORSA/TIMS Joint National Meeting in Miami
  Beach, FL, USA}, School of Industrial and Systems Engineering, Georgia
  Technology Institute, Atlanta, GA~30322--0205, USA, October 1986.

\bibitem{ipm:Tovey2}
C.~A. Tovey.
\newblock The challenge\,: {Teaching Karmarkar's} algorithm.
\newblock {\em OR/MS Today}, 15(2):18--19, April 1988.

\bibitem{ipm:Trafalis2}
T.~B. Trafalis.
\newblock {\em Efficient faces of a polytope\,: {Interior} methods in multiple
  objective optimization}.
\newblock PhD thesis, Department of Mathematics and Computer Science, School of
  Industrial Engineering, Purdue University, West Lafayette, IN~47907, USA,
  August 1989.

\bibitem{ipm:Trafalis3}
T.~B. Trafalis.
\newblock Interior point methods in backpropagation neural networks.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, School of Industrial Engineering, University of Oklahoma, Norman,
  OK~73019, USA, November 1991.

\bibitem{ipm:Trafalis4}
T.~B. Trafalis.
\newblock A method of centers that computes {Pareto} solutions of cooperative
  games in polynomial time.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, School of Industrial Engineering, University of Oklahoma, Norman,
  OK~73019, USA, April 1992.

\bibitem{ipm:Trafalis5}
T.~B. Trafalis and N.~P. Cou{\"e}llan.
\newblock Neural network training via a primal--dual interior point method for
  linear programming.
\newblock In {\em Proceedings of the World Congress on Neural Networks, Vol. 2
  (San Diego, June 1994)}, pages 798--803. Lawrence Erlbaum Associates,
  Hillsdale, NJ, USA, 1994.

\bibitem{ipm:Trafalis6}
T.~B. Trafalis and N.~P. Cou{\"e}llan.
\newblock Neural network training via an affine scaling quadratic optimization
  algorithm.
\newblock {\em Neural Networks}, 9:475--481, 1996.

\bibitem{ipm:Trafalis10}
T.~B. Trafalis, N.~P. Couellan, and S.~C. Bertrand.
\newblock Training of supervised neural networks via a nonlinear primal--dual
  interior--point method.
\newblock {\em IEEE Proceedings of the International Conference on Neural
  Networks}, pages 2017--2031, 1997.

\bibitem{ipm:Trafalis1}
T.~B. Trafalis and T.~L. Morin.
\newblock Interior point methods in multiobjective convex optimization.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, School of Industrial Engineering, University of Oklahoma,
  Norman, OK~73019, USA, July 1991.

\bibitem{ipm:Trafalis7}
T.~B. Trafalis and R.~K. Parekh.
\newblock Primal--dual training of artificial neural networks with an
  $l_{\infty}$ error.
\newblock {\em Proceedings of the Conference on Artificial Neural Networks in
  Engineering (ANNIE\,'95)}, pages 233--238, 1995.

\bibitem{ipm:Trafalis9}
T.~B. Trafalis, T.~Terlaky, J.~P. Warners, and C.~Roos.
\newblock Unsupervised neural network training via a potential reduction
  approach.
\newblock {Technical Report} 96--172, Faculty of Technical Mathematics and
  Informatics, Delft University of Technology, NL--2600 Delft, The Netherlands,
  1996.

\bibitem{ipm:Trafalis8}
T.~B. Trafalis, T.~A. Tutunji, and N.~P. Cou{\"e}llan.
\newblock Interior point methods for supervised training of artificial neural
  networks with bounded weights.
\newblock In P.~M. Pardalos, D.~W. Hearn, and W.~W. Hager, editors, {\em
  Network Optimization}, volume 450 of {\em Lecture Notes in Economics and
  Mathematical Syxstems}, pages 441--470. Springer Verlag, Berlin, Germany,
  1997.

\bibitem{ipm:Tsao1}
H.-S.~J. Tsao and S.-C. Fang.
\newblock An unconstrained dual approach to solving {Karmarkar--type} linear
  programs using conventional barrier functions.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 42:325--343, 1995.

\bibitem{ipm:Tseng1}
P.~Tseng.
\newblock A simple complexity proof for a polynomial--time linear programming
  algorithm.
\newblock {\em Operations Research Letters}, 8:155--159, 1989.

\bibitem{ipm:Tseng5}
P.~Tseng.
\newblock Path following by alternating minimization.
\newblock {Technical Report}, Department of Mathematics, GN--50, University of
  Washington, Seattle, WA~98195, USA, April 1991.

\bibitem{ipm:Tseng6}
P.~Tseng.
\newblock Complexity analysis of a linear complementarity algorithm based on a
  {Lyapunov} function.
\newblock {\em Mathematical Programming}, 53:297--306, 1992.

\bibitem{ipm:Tseng2}
P.~Tseng.
\newblock Global linear convergence of a path--following algorithm for some
  monotone variational inequality problems.
\newblock {\em Journal of Optimization Theory and Applications},
  75(2):265--279, 1992.

\bibitem{ipm:Tseng4}
P.~Tseng.
\newblock A path--following algorithm for linear programming using quadratic
  and logarithmic penalty functions.
\newblock {\em SIAM Journal on Control and Optimization}, 31:1578--1598, 1993.

\bibitem{ipm:Tseng7}
P.~Tseng.
\newblock Partial affine scaling for linearly constrained minimization.
\newblock {\em Mathematics of Operations Research}, 20:678--694, 1995.

\bibitem{ipm:Tseng8}
P.~Tseng.
\newblock Simplified analysis of an $o(nl)$--iteration infeasible
  predictor--corrector path--following method for monotone linear
  complementarity problems.
\newblock In R.~P. Agarwal, editor, {\em Recent Trends in Optimization Theory
  and Applications}, volume~5 of {\em World Science Series in Applied
  Analysis}, pages 423--434. World Science Publishing, River Edge, NJ, USA,
  1995.

\bibitem{ipm:Tseng9}
P.~Tseng.
\newblock Search directions and convergence analysis of some infeasible
  path--following methods for the monotone semi--definite {LCP}.
\newblock {Technical Report}, Department of Mathematics, GN--50, University of
  Washington, Seattle, WA~98195, USA, 1996.

\bibitem{ipm:Tseng10}
P.~Tseng.
\newblock Analysis of an infeasible interior path--following method for
  complementarity problems.
\newblock {Technical Report}, Department of Mathematics, GN--50, University of
  Washington, Seattle, WA~98195, USA, August 1997.
\newblock Revised September 1997.

\bibitem{ipm:Tseng3}
P.~Tseng and Z.~Q. Luo.
\newblock On the convergence of the affine--scaling algorithm.
\newblock {\em Mathematical Programming}, 52:301--319, 1992.

\bibitem{ipm:Tsuchiya5}
T.~Tsuchiya.
\newblock Dual standard form linear programming problems and {Karmarkar's}
  canonical form.
\newblock {\em Lecture Note of the Research Institute of Statistical
  Mathematics}, 676:330--336, 1988.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya4}
T.~Tsuchiya.
\newblock On {Yamashita's method and Freund's method} for linear programming.
\newblock {\em Cooperative Research Report of the Institute of Statistical
  Mathematics}, 10:105--115, 1988.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya3}
T.~Tsuchiya.
\newblock Degenerate linear programming problems and the affine scaling method.
\newblock {\em Systems, Control and Information}, 34(4):216--222, April 1990.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya1}
T.~Tsuchiya.
\newblock Global convergence of the affine scaling methods for degenerate
  linear programming problems.
\newblock {\em Mathematical Programming}, 52:377--404, 1991.

\bibitem{ipm:Tsuchiya7}
T.~Tsuchiya.
\newblock Local analysis of {Iri and Imai's} method for degenerate linear
  programming problems.
\newblock {Research Memorandum (in preparation)}, The Institute of Statistical
  Mathematics, 4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, 1991.
\newblock This report has been finished as Tsuchiya \cite{ipm:Tsuchiya8}.

\bibitem{ipm:Tsuchiya9}
T.~Tsuchiya.
\newblock {\em A study on the global and local convergence properties of the
  interior point algorithms for linear programming}.
\newblock PhD thesis, Faculty of Engineering, The University of Tokyo, Tokyo,
  Japan, 1991.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya6}
T.~Tsuchiya.
\newblock Global convergence property of the affine scaling methods for primal
  degenerate linear programming problems.
\newblock {\em Mathematics of Operations Research}, 17(3):527--557, 1992.

\bibitem{ipm:Tsuchiya11}
T.~Tsuchiya.
\newblock Global convergence of the affine scaling algorithm for primal
  degenerate strictly convex quadratic programming problems.
\newblock {\em Annals of Operations Research}, 46/47:509--539, 1993.

\bibitem{ipm:Tsuchiya15}
T.~Tsuchiya.
\newblock A new family of polynomial--time interior point algorithms for linear
  programming.
\newblock {Research Memorandum (in preparation)}, The Institute of Statistical
  Mathematics, 4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, 1994.

\bibitem{ipm:Tsuchiya13}
T.~Tsuchiya.
\newblock Theoretical analysis of an affine scaling algorithm\,: {The} interior
  point method and a duality theorem.
\newblock {\em Proceedings of the Institute of Statistical Mathematics},
  42:277--296, 1994.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya8}
T.~Tsuchiya.
\newblock Quadratic convergence of {Iri--Imai's} method for degenerate linear
  programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 87:703--726,
  1995.

\bibitem{ipm:Tsuchiya14}
T.~Tsuchiya.
\newblock Affine scaling algorithm.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 35--82. Kluwer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Tsuchiya16}
T.~Tsuchiya.
\newblock A polynomial primal--dual path--following algorithm for second--order
  cone programming.
\newblock {Research Memorandum} 649, The Institute of Statistical Mathematics,
  4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, October 1997.

\bibitem{ipm:Tsuchiya17}
T.~Tsuchiya.
\newblock A convergence analysis of the scaling--invariant primal--dual
  path--following algorithms for second--order cone programming.
\newblock {Research Memorandum} 664, The Institute of Statistical Mathematics,
  4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, 1998.

\bibitem{ipm:Tsuchiya12}
T.~Tsuchiya and R.~D.~C. Monteiro.
\newblock Superlinear convergence of the affine scaling algorithm.
\newblock {\em Mathematical Programming}, 75:77--110, 1996.

\bibitem{ipm:Tsuchiya10}
T.~Tsuchiya and M.~Muramatsu.
\newblock Global convergence of the long--step affine scaling algorithm for
  degenerate linear programming problems.
\newblock {\em SIAM Journal on Optimization}, 5:525--551, 1995.

\bibitem{ipm:Tsuchiya2}
T.~Tsuchiya and K.~Tanabe.
\newblock Local convergence properties of new methods in linear programming.
\newblock {\em Journal of the Operations Research Society of Japan}, 33:22--45,
  1990.

\bibitem{ipm:Tuncel2}
L.~Tun{\c{c}}el.
\newblock A note on the primal--dual affine scaling algorithms.
\newblock {Technical Report} 92--8, Computational Optimization Project, Center
  for Applied Mathematics, Cornell University, Ithaca, NY~14853--3801, USA, May
  1992.
\newblock For generalizations and extensions see Tun{\c{c}}el
  \cite{ipm:Tuncel4}.

\bibitem{ipm:Tuncel5}
L.~Tun{\c{c}}el.
\newblock A pseudo--polynomial complexity analysis for interior--point
  algorithms.
\newblock {Research Report} CORR\,93--16, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, 1993.

\bibitem{ipm:Tuncel4}
L.~Tun{\c{c}}el.
\newblock Constant potential primal--dual algorithms\,: {A} framework.
\newblock {\em Mathematical Programming}, 66:145--159, 1994.

\bibitem{ipm:Tuncel1}
L.~Tun{\c{c}}el.
\newblock On the convergence of primal--dual interior point methods with wide
  neighborhoods.
\newblock {\em Computational Optimization and Applications}, 4:139--158, 1995.

\bibitem{ipm:Tuncel6}
L.~Tun{\c{c}}el.
\newblock On the interplay among entropy, variable metrics and potential
  functions in interior--point algorithms.
\newblock {Research Report} CORR\,95--20, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, September 1995.
\newblock Also available as\,: Technical Report 1135, School of Operations
  Research and Industrial Engineering, Cornell University, Ithaca, NY~14853,
  USA, September 1995. See also Tun{\c{c}}el and Todd \cite{ipm:Tuncel8}.

\bibitem{ipm:Tuncel7}
L.~Tun{\c{c}}el.
\newblock Primal--dual symmetry and scale invariance of interior--point
  algorithms for convex optimization.
\newblock {Research Report} CORR\,96--18, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, November 1996.

\bibitem{ipm:Tuncel9}
L.~Tun{\c{c}}el.
\newblock On the condition numbers for polyhedra in {Karmarkar's} form.
\newblock {Research Report} CORR\,97--24, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario~N2L\,3G1, Canada, November 1997.

\bibitem{ipm:Tuncel12}
L.~Tun{\c{c}}el.
\newblock Approximating the complexity measure of vavasis--ye algorithm is
  {NP--hard}.
\newblock {Research Report} CORR~98--51, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario~N2L\,3G1, Canada, November 1998.

\bibitem{ipm:Tuncel11}
L.~Tun{\c{c}}el.
\newblock Convex optimization: {Barrier} functions and interior-point methods.
\newblock {Research Report} B--336, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario~N2L\,3G1, Canada, March 1998.

\bibitem{ipm:Tuncel10}
L.~Tun{\c{c}}el.
\newblock Primal-dual potential reduction algorithms for semidefinite
  programming.
\newblock {Research Report}, Department of Combinatorics and Optimization,
  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario~N2L\,3G1,
  Canada, March 1998.
\newblock To appear as {\em{Potential reduction and primal-dual methods}},
  Semidefinite Programming and Applications, R. Saigal, L. Vandenberghe and H.
  Wolkowicz (eds.), Kluwer Academic Publishers, Boston, MA, USA.

\bibitem{ipm:Tuncel3}
L.~Tun{\c{c}}el and M.~J. Todd.
\newblock Asymptotic behavior of interior--point methods\,: {A} view from
  semi--infinite programming.
\newblock {\em Mathematics of Operations Research}, 21:354--381, 1996.

\bibitem{ipm:Tuncel8}
L.~Tun{\c{c}}el and M.~J. Todd.
\newblock On the interplay among entropy, variable metrics and potential
  functions in interior--point algorithms.
\newblock {\em Computational Optimization and Its Applications}, 8:5--19, 1997.
\newblock See also Tun{\c{c}}el \cite{ipm:Tuncel6}.

\bibitem{ipm:Turner1}
K.~Turner.
\newblock A variable metric variant of the {Karmarkar} algorithm for linear
  programming.
\newblock {Technical Report} TR--87--13, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1987.

\bibitem{ipm:Turner2}
K.~Turner.
\newblock Computing projections for the {Karmarkar} algorithm.
\newblock {\em Linear Algebra and Its Applications}, 152:141--154, 1991.

\bibitem{ipm:Tutuncu1}
R.~T{\"u}t{\"u}nc{\"u}.
\newblock An infeasible--interior--point potential--reduction algorithm for
  linear programming.
\newblock {Technical Report} 1136, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, March 1996.

\bibitem{ipm:Tuetuencue1}
R.~H. T{\"u}t{\"u}nc{\"u} and M.~J. Todd.
\newblock Reducing horizontal linear complementarity problems.
\newblock {\em Linear Algebra and Its Applications}, 223/224:717--729, 1995.

\bibitem{ipm:Ulbrich2}
M.~Ulbrich and S.~Ulbrich.
\newblock Superlinear convergence of affine--scaling interior--point {Newton}
  methods for infinite--dimensional problems with pointwise bounds.
\newblock {Technical Report} TR~97--05, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1997.

\bibitem{ipm:Ulbrich1}
M.~Ulbrich, S.~Ulbrich, and M.~Heinkenschloss.
\newblock Global convergence of trust--region interior--point algorithms for
  infinite--dimensional nonconvex minimization subject to pointwise bounds.
\newblock {Technical Report} TR~97--04, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, March 1997.

\bibitem{ipm:Urban1}
T.~Urban, A.~Tits, and C.~Lawrence.
\newblock A primal--dual interior--point method for nonconvex optimization with
  multiple logarithmic barrier parameters and with strong convergence
  properties.
\newblock {Technical Report} TR~98--27, Institute for Systems Research,
  University of Maryland, College Park, 1998.

\bibitem{ipm:Vaidya1}
P.~M. Vaidya.
\newblock Linear programming and the center of a polytope.
\newblock {Technical Report}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974,
  USA, 1988.

\bibitem{ipm:Vaidya2}
P.~M. Vaidya.
\newblock A locally well--behaved potential function and a simple
  {Newton}--type method for finding the center of a polytope.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 79--90. Springer Verlag, New York,
  1989.

\bibitem{ipm:Vaidya4}
P.~M. Vaidya.
\newblock An algorithm for linear programming which requires ${O((m + n)n^2 +
  (m + n)^{1.5}nL)}$ arithmetic operations.
\newblock {\em Mathematical Programming}, 47:175--201, 1990.
\newblock Condensed version in\,: {\em Proceedings of the 19th Annual ACM
  Symposium on Theory of Computing, 29--38, 1987}.

\bibitem{ipm:Vaidya7}
P.~M. Vaidya.
\newblock A new algorithm for minimizing a convex function over convex sets.
\newblock In {\em Proceedings of the 30th Annual Symposium on Foundations of
  Computer Science\,(Research Triangle Park, NC, USA, 1989)}, pages 338--343.
  IEEE Computer Society Press, Los Alamitos, CA, USA, 1990.
\newblock See also Vaidya \cite{ipm:Vaidya3}.

\bibitem{ipm:Vaidya5}
P.~M. Vaidya.
\newblock Reducing the parallel complexity of certain linear programming
  problems.
\newblock In {\em Proceedings of the 22nd Annual Symposium on Foundations of
  Computer Science\,(St.\,Louis, MO, USA, October 1990)}, pages 583--589. IEEE
  Computer Society Press, Los Alamitos, CA, USA, 1990.

\bibitem{ipm:Vaidya6}
P.~M. Vaidya.
\newblock Speeding--up linear programming using fast matrix multiplication.
\newblock In {\em Proceedings of the 30th Annual Symposium on Foundations of
  Computer Science\,(Research Triangle Park, NC, USA, 1989)}, pages 332--337.
  IEEE Computer Society Press, Los Alamitos, CA, USA, 1990.

\bibitem{ipm:Vaidya3}
P.~M. Vaidya.
\newblock A new algorithm for minimizing a convex function over convex sets.
\newblock {\em Mathematical Programming}, 73:291--341, 1996.
\newblock A condensed version is given in Vaidya \cite{ipm:Vaidya7}.

\bibitem{ipm:Vaidya8}
P.~M. Vaidya and D.~S. Atkinson.
\newblock A technique for bounding the number of iterations in path following
  algorithms.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 462--489. World Scientific Publishing Co., London,
  United Kingdom, 1993.

\bibitem{ipm:Vandenberghe2}
L.~Vandenberghe and S.~Boyd.
\newblock A polynomial--time algorithm for determining quadratic {Lyapunov}
  functions for nonlinear systems.
\newblock {\em Proceedings of the European Conference on Circuit Theory and
  Design}, pages 1065--1068, 1993.

\bibitem{ipm:Vandenberghe1}
L.~Vandenberghe and S.~Boyd.
\newblock A primal--dual potential reduction method for problems involving
  matrix inequalities.
\newblock {\em Mathematical Programming}, 69:205--236, 1995.

\bibitem{ipm:Vandenberghe4}
L.~Vandenberghe and S.~Boyd.
\newblock Semidefinite programming.
\newblock {\em SIAM Review}, 38:49--95, 1996.

\bibitem{ipm:Vandenberghe3}
L.~Vandenberghe, S.~Boyd, and S.-P. Wu.
\newblock Determinant maximation with linear matrix inequality constraints.
\newblock {ISL--Report}, Department of Electrical Engineering, Information
  Systems Laboratory, Stanford University, Stanford, CA~94305, USA, March 1996.

\bibitem{ipm:Vandenberghe5}
L.~Vandenberghe and S.~Boydand A.~El Gamas.
\newblock Optimizing dominant tome constant in {RC} circuits.
\newblock {\em IEEE Transactions on Computer--Aided DEsign of Integrated
  Circuits and Systems}, 17:110--125, 1998.

\bibitem{ipm:Vanderbei1}
R.~J. Vanderbei.
\newblock A rescaled orthant variant of {Karmarkar's} algorithm.
\newblock {Technical Report}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733,
  USA, 1986.

\bibitem{ipm:Vanderbei2}
R.~J. Vanderbei.
\newblock The affine--scaling algorithm and primal degeneracy.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
  Mathematical Programming, Asimolar Conference Center, Pacific Grove, CA,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA, 1987.

\bibitem{ipm:Vanderbei3}
R.~J. Vanderbei.
\newblock Methods and apparatus for efficient resource allocation.
\newblock U.S.~Patent No.~4.744.026, 1988.
\newblock AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA.

\bibitem{ipm:Vanderbei4}
R.~J. Vanderbei.
\newblock Affine--scaling for linear programs with free variables.
\newblock {\em Mathematical Programming}, 43:31--44, 1989.

\bibitem{ipm:Vanderbei5}
R.~J. Vanderbei.
\newblock New developments in the affine--scaling algorithm for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA, October 1989.

\bibitem{ipm:Vanderbei19}
R.~J. Vanderbei.
\newblock {Interior--point methods for mathematical programming\,: Theory and
  practice}.
\newblock {Unpublished Manuscript}, Department of Civil Engineering and
  Operations Research, Princeton University, Princeton, NJ~08544, USA, 1990.

\bibitem{ipm:Vanderbei13}
R.~J. Vanderbei.
\newblock {Performance of the AT~\&~T KORBX System}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA, May 1990.

\bibitem{ipm:Vanderbei14}
R.~J. Vanderbei.
\newblock {A brief description of ALPO}.
\newblock {\em Operations Research Letters}, 10:531--534, 1991.
\newblock See also Vanderbei\,\cite{ipm:Vanderbei12}.

\bibitem{ipm:Vanderbei15}
R.~J. Vanderbei.
\newblock Dense columns and interior--point methods for {LP}.
\newblock In {\em Proceedings of the IMACS'91 World Congress on Computation and
  Applied Mathematics in Dublin, Ireland}, July 1991.

\bibitem{ipm:Vanderbei8}
R.~J. Vanderbei.
\newblock Efficient handling of dense columns in linear and quadratic programs.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, AT~\&~T Bell Laboratories, 10~Knob Hill Road, Morganville,
  NJ~07751, USA, July 1991.

\bibitem{ipm:Vanderbei9}
R.~J. Vanderbei.
\newblock Splitting dense columns in sparse linear systems.
\newblock {\em Linear Algebra and Its Applications}, 152:107--117, 1991.

\bibitem{ipm:Vanderbei18}
R.~J. Vanderbei.
\newblock {LOQO User's Manual}.
\newblock {Technical Report} SOL~92--05, Department of Civil Engineering and
  Operations Research, Princeton University, Princeton, NJ~08544, USA, 1992.
\newblock See also Vanderbei \cite{ipm:Vanderbei23,ipm:Vanderbei24}.

\bibitem{ipm:Vanderbei17}
R.~J. Vanderbei.
\newblock Primal--dual symmetric formulations of the predictor--corrector
  method for {QP}.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, May 1992.

\bibitem{ipm:Vanderbei16}
R.~J. Vanderbei.
\newblock Robust optimization\,: {Solution} methologies with interior point
  methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, April 1992.

\bibitem{ipm:Vanderbei12}
R.~J. Vanderbei.
\newblock {ALPO\,: Another} linear program optimizer.
\newblock {\em ORSA Journal on Computing}, 5:134--146, 1993.
\newblock See also Vanderbei\,\cite{ipm:Vanderbei14}.

\bibitem{ipm:Vanderbei21}
R.~J. Vanderbei.
\newblock Interior--point methods\,: {Algorithms} and formulations.
\newblock {\em ORSA Journal on Computing}, 6:32--34, 1994.

\bibitem{ipm:Vanderbei20}
R.~J. Vanderbei.
\newblock Affine--scaling trajectories associated with a semi--infinite linear
  program.
\newblock {\em Mathematics of Operations Research}, 20:163--174, 1995.

\bibitem{ipm:Vanderbei23}
R.~J. Vanderbei.
\newblock {LOQO\,: An} interior point code for quadratic programming.
\newblock {Technical Report} SOR--94--15, Department of Civil Engineering and
  Operations Research, Program in Statistics and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, February 1995.
\newblock See also Vanderbei \cite{ipm:Vanderbei18,ipm:Vanderbei24}.

\bibitem{ipm:Vanderbei10}
R.~J. Vanderbei.
\newblock Symmetric quasidefinite matrices.
\newblock {\em SIAM Journal on Optimization}, 5:100--113, 1995.

\bibitem{ipm:Vanderbei25}
R.~J. Vanderbei.
\newblock {\em Linear Programming\,: Foundations and Extensions}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Vanderbei24}
R.~J. Vanderbei.
\newblock {LOQO User's Manual--Version\,2.21}.
\newblock {Technical Report} SOL~96--07, Department of Civil Engineering and
  Operations Research, Princeton University, Princeton, NJ~08544, USA, 1996.
\newblock See also Vanderbei \cite{ipm:Vanderbei18,ipm:Vanderbei23}.

\bibitem{ipm:Vanderbei11}
R.~J. Vanderbei and T.~J. Carpenter.
\newblock Symmetric indefinite systems for interior point methods.
\newblock {\em Mathematical Programming}, 58:1--32, 1993.

\bibitem{ipm:Vanderbei22}
R.~J. Vanderbei, A.~Duarte, and B.~Yang.
\newblock An algorithmic and numerical comparison of several interior--point
  methods.
\newblock {Technical Report} SOR--94--05, Department of Civil Engineering and
  Operations Research, Program in Statistics and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, July 1994.

\bibitem{ipm:Vanderbei6}
R.~J. Vanderbei and J.~C. Lagarias.
\newblock {I.\,I.\,Dikin's} convergence result for the affine--scaling
  algorithm.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 109--119. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Vanderbei7}
R.~J. Vanderbei, M.~S. Meketon, and B.~A. Freedman.
\newblock A modification of {Karmarkar's} linear programming algorithm.
\newblock {\em Algorithmica}, 1(4):395--407, 1986.

\bibitem{ipm:Vanderbei26}
R.~J. Vanderbei and D.~F. Shanno.
\newblock An interior point algorithm for nonconvex nonlinear programming.
\newblock {Technical Report} SOR--97--21, Department of Civil Engineering and
  Operations Research, Princeton University, Princeton, NJ~08544, USA, 1997.
\newblock Revised May 1998.

\bibitem{ipm:Vanderbei27}
R.~J. Vanderbei and H.~Yurttan.
\newblock Using {LOQO} to solve second--order cone programming problems.
\newblock {Technical Report} SOR--98--9, Department of Civil Engineering and
  Operations Research, Princeton University, Princeton, NJ~08544, USA, 1998.

\bibitem{ipm:Vannelli1}
A.~Vannelli.
\newblock An interior point method for solving the global routing problem.
\newblock In {\em Proceedings of the IEEE Custom Integrated Circuits
  Conference, San Diego, CA, USA, May 1988}, pages 3.4.1--3.4.4, 1989.

\bibitem{ipm:Vannelli3}
A.~Vannelli.
\newblock An adaptation of the interior point method for solving the global
  routing problem.
\newblock {\em IEEE Transactions on Computer--Aided Design of Integrated
  Circuits and Systems}, 10(2):193--203, February 1991.

\bibitem{ipm:Vannelli5}
A.~Vannelli.
\newblock A parallel implementation of an interior point method for linear
  programming.
\newblock In J.~Dongarra, K.~Kennedy, P.~Messina, D.~C. Sorrensen, and R.~G.
  Voigt, editors, {\em Parallel Processing for Scientific Computing
  (Proceedings of the Fifth SIAM Conference held in Houston, Texas, USA,
  1991)}, pages 163--167, Philadelphia, PA, USA, 1992. SIAM Publications.

\bibitem{ipm:Vannelli6}
A.~Vannelli.
\newblock Teaching large--scale optimization by an interior point approach.
\newblock {\em IEEE Transactions on Education (E)}, 36:204--209, 1993.

\bibitem{ipm:Vannelli7}
A.~Vannelli, A.~Kennings, and P.~Chin.
\newblock Interior point approaches for the {VLSI} placement problem.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 501--528. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Vannelli2}
A.~Vannelli and E.~Klein.
\newblock A {Cholesky}--conjugate gradient implementation of {Karmarkar's}
  algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Faculty of Engineering, Department of Electrical Engineering,
  University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, April 1988.

\bibitem{ipm:Vannelli4}
A.~Vannelli, L.~Vargas, and V.~H. Quintana.
\newblock Interior point optimization methods\,: {Theory}, implementations and
  engineering applications.
\newblock {\em Canadian Journal of Electrical and Computer Engineering},
  117:84--94, 1992.

\bibitem{ipm:Vargas1}
L.~S. Vargas, V.~H. Quintana, and A.~Vannelli.
\newblock A tutorial description of an interior point method and its
  applications to security--constrained economic dispatch.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 8:1315--1324, 1993.

\bibitem{ipm:Vassiliadis1}
V.~S. Vassiliadis.
\newblock Application of the modified barrier method in large--scale quadratic
  problems.
\newblock {\em Computers and Chemical Engineering}, 20:S243--S248, 1996.

\bibitem{ipm:Vassiliadis2}
V.~S. Vassiliadis and C.~A. Floudas.
\newblock The modified barrier function approach for large--scale optimization.
\newblock {\em Computers and Chemical Engineering}, 21:855--874, 1997.

\bibitem{ipm:Vavasis1}
S.~A. Vavasis and Y.~Ye.
\newblock An accelerated interior point method whose running time depends only
  on {$A$}.
\newblock {Technical Report} 93--1391, Department of Computer Science, Upson
  Hall, Cornell University, Ithaca, NY~14853, USA, 1993.
\newblock Extended abstract in\,: {\em Proceedings of the Twenty--Sixth Annual
  ACM Symposium on the Theory of Computing, pp. 512--520, 1993}.

\bibitem{ipm:Vavasis2}
S.~A. Vavasis and Y.~Ye.
\newblock A primal--dual accelerated interior point method whose running time
  depends only on {$A$}.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, December 1994.
\newblock Simplified version of Vavasis and Ye \cite{ipm:Vavasis1}. See also
  Vavasis and Ye \cite{ipm:Vavasis5,ipm:Vavasis7}.

\bibitem{ipm:Vavasis4}
S.~A. Vavasis and Y.~Ye.
\newblock Condition numbers for polyhedra with real number data.
\newblock {\em Operations Research Letters}, 17:209--214, 1995.

\bibitem{ipm:Vavasis3}
S.~A. Vavasis and Y.~Ye.
\newblock Identifying an optimal basis in linear programming.
\newblock {\em Annals of Operations Research}, 62:565--572, 1996.

\bibitem{ipm:Vavasis6}
S.~A. Vavasis and Y.~Ye.
\newblock On the relationship between layered least squares and affine scaling
  steps.
\newblock In J.~Renegar, M.~Shub, and S.~Smale, editors, {\em The Mathematics
  of Numerical Analysis (1995 AMS--SIAM Summer Seminar in Applied Mathematics
  July/August 1995 held at Park City, UT, USA)}, volume~32 of {\em Lectures in
  Applied Mathematics}, pages 857--865. American Mathematical Society,
  Providence, RI~02940--6248, USA, 1996.

\bibitem{ipm:Vavasis5}
S.~A. Vavasis and Y.~Ye.
\newblock A primal--dual interior point method whose running time depends only
  on the constraint matrix.
\newblock {\em Mathematical Programming}, 74:79--120, 1996.
\newblock See also Vavasis and Ye\,\cite{ipm:Vavasis7}.

\bibitem{ipm:Vavasis7}
S.~A. Vavasis and Y.~Ye.
\newblock A simplification to\,: {A} primal--dual interior point method whose
  running time depends only on the constraint matrix.
\newblock {Technical Note}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, January 1997.
\newblock See also Vavasis and Ye \cite{ipm:Vavasis1,ipm:Vavasis2,%
  ipm:Vavasis5}.

\bibitem{ipm:Venkaiah1}
V.~C. Venkaiah.
\newblock An efficient algorithm for linear programming.
\newblock {\em Proceedings of the Indian Academy of Sciences, Mathematical
  Sciences}, 100(3):205--301, 1990.
\newblock See also K{\"a}schel\,\cite{ipm:Kaeschel2}.

\bibitem{ipm:Venkaiah2}
V.~C. Venkaiah.
\newblock Deriving {Karmarkar's} {LP} algorithm using angular projection
  matrix.
\newblock {\em Proceedings of the Indian Academy of Sciences, Mathematical
  Sciences}, 106:69--77, 1996.

\bibitem{ipm:Vera1}
J.~R. Vera.
\newblock Ill--posedness and finite precision arithmetic\,: {A} complexity
  analysis of interior point methods.
\newblock In F.~Cucker and M.~Shub, editors, {\em Foundations of Computational
  Mathematics}, pages 424--433. Springer Verlag, Berlin, Germany, 1997.

\bibitem{ipm:Vera2}
J.~R. Vera.
\newblock On the complexity of linear programming under finite precision
  arithmetic.
\newblock {\em Mathematical Programming}, 80:91--123, 1998.

\bibitem{ipm:Vial2}
J.-Ph. Vial.
\newblock A fully polynomial-time projective method.
\newblock {\em Operations Research Letters}, 7:15--19, 1988.

\bibitem{ipm:Vial1}
J.-Ph. Vial.
\newblock Approximate projections in a projective method for the linear
  feasibility problem.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 65--78. Springer Verlag, New York,
  1989.

\bibitem{ipm:Vial3}
J.-Ph. Vial.
\newblock A unified approach to projective algorithms for linear programming.
\newblock In S.~Dolecki, editor, {\em Optimization\,: Proceedings of the 5th
  French--German Conference in Castel--Novel, Varetz, France, October 1988},
  volume 1405 of {\em Lecture Notes in Mathematics}, pages 191--220. Springer
  Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Vial4}
J.-Ph. Vial.
\newblock Decomposition of structured linear programs based on analytic
  centers.
\newblock volume 353 of {\em Lecture Notes in Economics and Mathematical
  Systems}, pages 190--203. Springer Verlag, Berlin, Germany, 1991.

\bibitem{ipm:Vial5}
J.-Ph. Vial.
\newblock Computational experience with a primal--dual interior--point method
  for smooth convex programming.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 583--586. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.
\newblock Full version in Vial \cite{ipm:Vial6}.

\bibitem{ipm:Vial6}
J.-Ph. Vial.
\newblock Computational experience with a primal--dual interior--point method
  for smooth convex programming.
\newblock {\em Optimization Methods and Software}, 3:285--310, 1994.
\newblock Condensed version in Vial \cite{ipm:Vial5}.

\bibitem{ipm:Vial7}
J.-Ph. Vial.
\newblock A generic path--following algorithm with a sliding constraint and its
  application to linear programming and the computation of analytic centers.
\newblock {Technical Report} 1996.8, Logilab, HEC Geneva, Section of Management
  Studies, University of Geneva, CH--1211~Geneva, Switzerland, 1996.

\bibitem{ipm:Vial8}
J.-Ph. Vial.
\newblock A path--following version of the {Todd--Burrell} procedure for linear
  programming.
\newblock {\em Mathematical Methods of Operations Research}, 46:153--167, 1997.

\bibitem{ipm:Vicente1}
L.~N. Vicente.
\newblock {\em Trust--region interior point algorithms for a class of nonlinear
  programming problems}.
\newblock PhD thesis, Department of Computational and Applied Mathematics, Rice
  University, Houston, TX~77251, USA, 1996.
\newblock Available as\,: Technical Report TR96--05.

\bibitem{ipm:Vicente2}
L.~N. Vicente.
\newblock On interior--point {Newton} algorithms for discretized optimal
  control problems with state constraints.
\newblock {\em ?}, ?:?, 1998.
\newblock Found in CMP (1998), p. 2182.

\bibitem{ipm:Villavicencio1}
J.~Villavicencio and M.~D. Grigoriadis.
\newblock Approximate {Langrangian} decomposition with a modified {Karmarkar}
  logarithmic potential.
\newblock In P.~M. Pardalos, D.~W. Hearn, and W.~W. Hager, editors, {\em
  Network Optimization}, volume 450 of {\em Lecture Notes in Economics and
  Mathematical Systems}, pages 471--485. Springer Verlag, Berlin, Germany,
  1997.

\bibitem{ipm:Vladimirou1}
H.~Vladimirou and S.~A. Zenios.
\newblock Scalable parallel computations for large--scale stochastic
  programming.
\newblock {Technical Report}, Department of Public and Business Administration,
  University of Cyprus, Nicosia, Cyprus, April 1996.

\bibitem{ipm:Vorst2}
{J. G. G. van de} Vorst.
\newblock A parallel implementation of the {Karmarkar} algorithm using a
  parallel linear algebra library.
\newblock In G.~A. van Zee and J.~G.~G. van~de Vorst, editors, {\em Parallel
  Computing 1988, Proceedings of the SHELL Conference, Amsterdam, The
  Netherlands, June 1988}, volume 384 of {\em Lecture Notes in Computer
  Science}, pages 127--135. Springer Verlag, Berlin, Germany, 1988.

\bibitem{ipm:Vorst1}
{J. G. G. van der} Vorst.
\newblock An attempt to use parallel computing in large scale optimisation.
\newblock In {C. F. H. van} Rijn, editor, {\em Logistics, Where Ends Have to
  Meet\,: Proceedings of the Shell Conference on Logistics in Apeldoorn, The
  Netherlands, November 1988}, pages 112--119. Pergamon Press, Oxford, United
  Kingdom, 1989.

\bibitem{ipm:Vucetic1}
V.~Vucetic.
\newblock Active set strategies in linear programming using barrier functions.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Energoinvest--Sou, Tvornicka~3, YU--71000~Sarajevo,
  Yugoslavia, July 1991.

\bibitem{ipm:Wallacher2}
C.~Wallacher.
\newblock {\em {Kombinatorische Algorithmen f{\"u}r Flu{\ss}probleme and
  submodulare Flu{\ss}probleme (Combinatorial algorithms for flow problems and
  submodular flow problems)}}.
\newblock PhD thesis, Faculty of Mathematics, Technical University of
  Braunschweig, Braunschweig, Germany, 1992.
\newblock (In German).

\bibitem{ipm:Wallacher1}
C.~Wallacher and U.~Zimmermann.
\newblock A combinatorial interior point method for network flow problems.
\newblock {\em Mathematical Programming}, 52:321--335, 1992.

\bibitem{ipm:Wang5}
S.~Q. Wang and Z.~L. Wei.
\newblock Parallel computation for linear programming with the interior point
  method.
\newblock {\em Journal on Numerical Methods and Computations with
  Applications}, 17:57--63, 1996.
\newblock (In Chinese).

\bibitem{ipm:Wang4}
T.~Wang, R.~D.~C. Monteiro, and J.-S. Pang.
\newblock An interior point potential reduction method for constrained
  equations.
\newblock {\em Mathematical Programming}, 74:159--195, 1996.

\bibitem{ipm:Wang1}
Y.~Wang.
\newblock {\em A study of projective algorithms for linear and convex quadratic
  programming}.
\newblock PhD thesis, School of Operations Research and Industrial Engineering,
  Cornell University, Ithaca, NY~14853--3801, USA, January 1992.

\bibitem{ipm:Wang2}
Y.~Wang, G.~C. Feng, and T.~Z. Liu.
\newblock An interior point algorithm for convex nonlinear programming
  problems.
\newblock {\em Numerical Mathematics (A Journal of Chinese Universities,
  English Series)}, 1(1):1--18, 1993.

\bibitem{ipm:Wang3}
Y.~Wang and H.~W. Zhang.
\newblock A new potential function for linear programming and its applications.
\newblock {\em Journal of Mathematical Research and Exposition}, 13:633--634,
  1993.
\newblock (In Chinese).

\bibitem{ipm:Wanka1}
A.~Wanka.
\newblock Interior and exterior methods for linear programming.
\newblock In D.~Pressmar, K.~E. Jaeger, H.~Krallmann, H.~Schellhaas, and
  L.~Streitfeldt, editors, {\em Operations Research Proceedings 1988}, pages
  214--221, Springer Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Warners1}
J.~P. Warners.
\newblock A potential reduction approach to the radio link frequency assignment
  problem.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics,
  Delft University of Technology, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Warners2}
J.~P. Warners, T.~Terlaky, C.~Roos, and B.~Jansen.
\newblock Potential reduction algorithms for structured combinatorial
  optimization problems.
\newblock {\em Operations Research Letters}, 21:55--64, 1997.

\bibitem{ipm:Warners3}
J.~P. Warners, T.~Terlaky, C.~Roos, and B.~Jansen.
\newblock A potential reduction approach to the frequency assignment problem.
\newblock {\em Discrete Applied Mathematics}, 78:251--282, 1997.

\bibitem{ipm:Wechs1}
M.~Wechs.
\newblock The analyticity of interior--point--paths at strictly complementarity
  solutions of linear programs.
\newblock {\em Optimization Methods and Software}, 9:209--243, 1998.

\bibitem{ipm:Wei10}
H.~Wei, H.~Sasaki, and J.~Kubokawa.
\newblock Interior point method for hydro--thermal optimal power flow.
\newblock {\em Proceedings of the 1995 International Conference on Energy
  Management and Power Delivery}, Part 2/2:607--612, 1995.

\bibitem{ipm:Wei15}
H.~Wei, H.~Sasaki, and J.~Kubokawa.
\newblock Decoupled solution of hydro--thermal optimal power flow problem by
  means of interior point method and network programming.
\newblock {\em IEEE Transactions on Power Systems}, 13:286--293, 1998.

\bibitem{ipm:Wei13}
H.~Wei, H.~Sasaki, J.~Kubokawa, and R.~Yokoyama.
\newblock Interior point nonlinear programming method for optimal power flow
  problems with a novel data structure.
\newblock {\em Proceedings of the 20th International Conference on Power
  Industry Computer Applications}, pages 134--141, 1996.

\bibitem{ipm:Wei14}
H.~Wei, H.~Sasaki, J.~Kubokawa, and R.~Yokoyama.
\newblock Interior--point method for power system nonlinear {$L_{1}$} norm
  static state estimation.
\newblock {\em IEEE Transactions on Power Systems}, 13:617--623, 1998.

\bibitem{ipm:Wei8}
H.~Wei, H.~Sasaki, and R.~Yokoyama.
\newblock Application of interior point quadratic algorithm to power system
  optimization problems.
\newblock {\em Proceedings of the 1995 IEEE Power Industry Computer Application
  Conference (Salt Lake City, UT, USA)}, pages 98--104, 1995.
\newblock See also Wei et al. \cite{ipm:Wei11}.

\bibitem{ipm:Wei11}
H.~Wei, H.~Sasaki, and R.~Yokoyama.
\newblock Application of interior point quadratic algorithm to power system
  optimization problems.
\newblock {\em IEEE Transactions on Power Systems}, 11:260--266, 1996.
\newblock See also Wei et al. \cite{ipm:Wei8}.

\bibitem{ipm:Wei1}
Z.-L. Wei.
\newblock An exact solution to linear programming using an interior point
  method.
\newblock {\em Journal of Computational Mathematics}, 5:264--271, 1987.

\bibitem{ipm:Wei2}
Z.-L. Wei.
\newblock An interior point method for linear programming.
\newblock {\em Journal of Computational Mathematics}, 5:342--351, 1987.

\bibitem{ipm:Wei3}
Z.-L. Wei.
\newblock Some recent developments in linear programming.
\newblock {\em Mathematics in Practice and Theory}, 3:82--89, 1988.
\newblock (In Chinese).

\bibitem{ipm:Wei7}
Z.-L. Wei.
\newblock An estimate of {Lagrange} multipliers for linear programming using
  interior--point methods.
\newblock {\em Chinese Sciences Bulletin}, 37:1334--1338, 1992.

\bibitem{ipm:Wei5}
Z.-L. Wei.
\newblock The decomposition principle and algorithms for linear programs under
  interior point method, {part~I}.
\newblock {\em Chinese Sciences Bulletin}, 38:1585--1590, 1993.

\bibitem{ipm:Wei6}
Z.-L. Wei.
\newblock The decomposition principle and algorithms for linear programs under
  interior point method, {part~II}.
\newblock {\em Chinese Sciences Bulletin}, 38:1591--1595, 1993.

\bibitem{ipm:Wei12}
Z.-L. Wei.
\newblock An optimal basis identification criterion for interior point linear
  programming algorithms.
\newblock {\em Mathematica Numerica Sinica}, 18:215--224, 1996.
\newblock (In Chinese).

\bibitem{ipm:Wei4}
Z.-L. Wei and L.~Wu.
\newblock Implementation of a dual interior algorithm for linear programming.
\newblock {\em Journal on Numerical Methods and Computer Applications},
  14(2):131--138, 1993.
\newblock (In Chinese).

\bibitem{ipm:Wei9}
Z.-L. Wei and L.~Wu.
\newblock A decomposition algorithm for linear programming under the interior
  point method and its parallel computation.
\newblock {\em Journal on Numerical Methods and Computer Applications},
  16:99--108, 1995.
\newblock (In Chinese).

\bibitem{ipm:Werner1}
J.~Werner.
\newblock {\em Numerische Mathematik~2 (Numerical Mathematics~2)}, chapter
  6.4\,: {Das Karmarkar Verfahren (The Karmarkar algorithm)}, pages 128--141.
\newblock Vieweg Verlag, Braunschweig, Germany, 1992.

\bibitem{ipm:Winston1}
W.~L. Whinston.
\newblock {\em Operations Research\,: Applications and Algorithms}, chapter
  4--13\,: {Karmarkar's} method for solving {LPs}, pages 178--179, chapter
  10--6~: {Karmarkar's} method for solving {LPs}, pages 569--574.
\newblock PWS--Kent Publishing Company, Boston, USA, second edition, 1992.

\bibitem{ipm:Whisman1}
A.~W. Whisman.
\newblock Optimization modelling in the military airlift command.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, CINCMAC Analysis Group, HQ~MAC/AG, Scott AFB, IL~62225, USA, May 1990.

\bibitem{ipm:White1}
D.~J. White.
\newblock Linear programming and {H}uard's method of centres.
\newblock {Working Paper}, Universities of Manchester and Virginia, Manchester,
  United Kingdom, 1989.

\bibitem{ipm:Wiegers1}
R.~M. Wiegers.
\newblock Implementation of the primal--dual interior point method for linear
  programming on a transputer network.
\newblock Master's thesis, Faculty of Electrical Engineering, Delft University
  of Technology, NL--2628~BL~Delft, The Netherlands, June 1990.

\bibitem{ipm:Wild1}
W.~G. Wild and O.~Port.
\newblock The startling discovery {Bell Labs} kept in the shadows.
\newblock {\em {Business Week}}, September 21st 1987.

\bibitem{ipm:Williams1}
R.~O. Williams.
\newblock An implementation of the affine scaling algorithm for linear
  programming problems with network constraints.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Management Science, California State University,
  Northridge, Los Angeles, CA~90024, USA, November 1991.

\bibitem{ipm:Wilson1}
J.~Wilson.
\newblock A barrier function approach to mixed integer programming.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Loughborough University, Loughborough, United Kingdom, January 1991.

\bibitem{ipm:Witzgall1}
C.~Witzgall, P.~T. Boggs, and P.~D. Domich.
\newblock On the convergence behavior of trajectories for linear programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 161--187. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Witzgall2}
C.~Witzgall, P.~T. Boggs, and P.~D. Domich.
\newblock On center trajectories and their relatives in linear programming.
\newblock {NISTIR Technical Report (in preparation)}, United States Department
  of Commerce, Applied and Computational Mathematics Division, National
  Institute of Standards and Technology, Gaithersburg, MD~20899, USA, 1991.
\newblock First draft in April 1988.

\bibitem{ipm:Wolkowicz1}
H.~Wolkowicz and A.~{Ben--Israel}.
\newblock A volume and constraint reducing algorithm for linear programming.
\newblock {Technical Report}, Department of Combinatorics and Optimization,
  University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1986.

\bibitem{ipm:Wolkowicz2}
H.~Wolkowicz and Q.~Zhao.
\newblock Semidefinite programming relaxations for the graph partitioning
  problem.
\newblock {Technical Report}, Department of Combinatorics and Optimization,
  University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, October 1996.

\bibitem{ipm:Wright6}
M.~H. Wright.
\newblock A brief history of linear programming.
\newblock {\em SIAM News}, 18(3):4, November 1985.

\bibitem{ipm:Wright1}
M.~H. Wright.
\newblock Issues of numerical analysis in barrier trajectory methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, October 1989.
\newblock See Wright \cite{ipm:Wright7,ipm:Wright9}, and Murray and Wright
  \cite{ipm:Murray3}.

\bibitem{ipm:Wright2}
M.~H. Wright.
\newblock Interior methods for nonlinearly constrained optimization.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, July 1990.
\newblock See Wright \cite{ipm:Wright7,ipm:Wright9}, and Murray and Wright
  \cite{ipm:Murray3}.

\bibitem{ipm:Wright4}
M.~H. Wright.
\newblock Strategies in path--following methods for nonlinear constraints.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, October
  1990.
\newblock See Wright \cite{ipm:Wright7,ipm:Wright9}, and Murray and Wright
  \cite{ipm:Murray3}.

\bibitem{ipm:Wright5}
M.~H. Wright.
\newblock Linear algebra issues in interior methods.
\newblock {Talk held at the Fourth SIAM Conference on Applied Linear Algebra in
  Minneapolis, MN, USA}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA,
  September 1991.
\newblock See Wright \cite[Section\ 7]{ipm:Wright9}.

\bibitem{ipm:Wright9}
M.~H. Wright.
\newblock Determining subspace information from the {Hessian} of a barrier
  function.
\newblock {Numerical Analysis Manuscript} 92--02, AT~\&~T~Bell Laboratories,
  Murray Hill, NJ~07974, USA, 1992.

\bibitem{ipm:Wright7}
M.~H. Wright.
\newblock Interior methods for constrained optimization.
\newblock In A.~Iserles, editor, {\em Acta Numerica~1992}, pages 341--407.
  Cambridge University Press, New York, USA, 1992.

\bibitem{ipm:Wright8}
M.~H. Wright.
\newblock Interior point methods for large--scale nonlinear optimization
  problems.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, May 1992.
\newblock See Wright \cite{ipm:Wright9}.

\bibitem{ipm:Wright11}
M.~H. Wright.
\newblock Some linear algebra issues in large--scale optimization.
\newblock In M.~S. Moonen, G.~H. Golub, and {B. L. R. De} Moor, editors, {\em
  Linear Algebra for Large Scale and Real--Time Applications (Leuven 1992)},
  volume 232 of {\em NATO Advanced Science Institutes Series E\,: Applied
  Sciences}, pages 315--337. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1993.

\bibitem{ipm:Wright10}
M.~H. Wright.
\newblock Some properties of the {Hessian} of the logarithmic barrier function.
\newblock {\em Mathematical Programming}, 67:265--295, 1994.

\bibitem{ipm:Wright3}
M.~H. Wright.
\newblock Why a pure primal {Newton} barrier step may be infeasible.
\newblock {\em SIAM Journal on Optimization}, 5:1--12, 1995.

\bibitem{ipm:Wright13}
M.~H. Wright.
\newblock The interior--point revolution in constrained optimization.
\newblock {Technical Report} 98--4--09, Computing Sciences Research Center,
  Bell Laboratories, Murray Hill, NJ~07974, USA, June 1998.

\bibitem{ipm:Wright12}
M.~H. Wright.
\newblock Ill--conditioning and computational error in interior--point methods
  for nonlinear programming.
\newblock {\em SIAM Journal on Optimization}, 9:84--111, 1999.

\bibitem{ipm:SWright3}
S.~J. Wright.
\newblock Structured interior point methods for optimal control.
\newblock {\em Proceedings of the 30th IEEE Conference on Decision and Control
  (Brighton, United Kingdom, December 1991)}, 2:1711--1716, 1991.

\bibitem{ipm:SWright6}
S.~J. Wright.
\newblock Convergence of an interior--point algorithm for linear
  complementarity problems under weak assumptions.
\newblock {Technical Report} MCS--P340--1192, Mathematical and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, October 1992.

\bibitem{ipm:SWright1}
S.~J. Wright.
\newblock An interior point algorithm for linearly constrained optimization.
\newblock {\em SIAM Journal on Optimization}, 2:450--473, 1992.

\bibitem{ipm:SWright4}
S.~J. Wright.
\newblock Structured interior point methods for stagewise extended linear
  quadratic programming {(ELQP)} problems.
\newblock {Talk held at the American Control Conference}, Mathematical and
  Computer Science Division, Argonne National Laboratory, Argonne, IL~60439,
  USA, June 1992.
\newblock {Technical Report} in preparation.

\bibitem{ipm:SWright2}
S.~J. Wright.
\newblock Interior point methods for optimal control of discrete--time systems.
\newblock {\em Journal of Optimization Theory and Applications}, 77:161--187,
  1993.

\bibitem{ipm:SWright8}
S.~J. Wright.
\newblock A path--following infeasible--interior--point algorithm for linear
  complementarity problems.
\newblock {\em Optimization Methods and Software}, 2:79--106, 1993.

\bibitem{ipm:SWright5}
S.~J. Wright.
\newblock An infeasible--interior--point algorithm for linear complementarity
  problems.
\newblock {\em Mathematical Programming}, 67:29--51, 1994.

\bibitem{ipm:SWright12}
S.~J. Wright.
\newblock Stability of linear algebra computations in interior--point methods
  for linear programming.
\newblock {Preprint} MCS--P446--0694, Mathematical and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, June 1994.
\newblock Revised July 1995.

\bibitem{ipm:SWright11}
S.~J. Wright.
\newblock Stability of linear equations solvers in interior--point methods.
\newblock {\em SIAM Journal on Matrix Analysis and Applications},
  16:1287--1307, 1995.

\bibitem{ipm:SWright14}
S.~J. Wright.
\newblock Modified {Cholesky} factorizations in interior--point algorithms for
  linear programming.
\newblock {Technical Report} ANL/MCS--P600--0596, Mathematical and Computer
  Science Division, Argonne National Laboratory, Argonne, IL~60439, USA, May
  1996.
\newblock Revised June 1998.

\bibitem{ipm:SWright10}
S.~J. Wright.
\newblock A path--following interior--point method for linear and quadratic
  problems.
\newblock {\em Annals of Operations Research}, 62:103--130, 1996.

\bibitem{ipm:SWright13}
S.~J. Wright.
\newblock {\em Primal--Dual Interior--Point Methods}.
\newblock SIAM Publications, SIAM, Philadelphia, PA, USA, 1996.

\bibitem{ipm:SWright16}
S.~J. Wright.
\newblock On the convergence of the {Newton}/log--barrier method.
\newblock {Preprint} ANL/MCS--P681--0897, Mathematical and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, August 1997.

\bibitem{ipm:SWright15}
S.~J. Wright.
\newblock Stability of augmented system factorizations in interior--point
  methods.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 18:191--222,
  1997.

\bibitem{ipm:SWright17}
S.~J. Wright.
\newblock Effects of finite--precision arithmetic on interior--point methods
  for nonlinear programming.
\newblock {Preprint} ANL/MCS--P705--0198, Mathematical and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, January 1998.

\bibitem{ipm:SWright18}
S.~J. Wright and F.~Jarre.
\newblock The role of linear objective functions in barrier methods.
\newblock {\em Mathematical Programming}, 84:357--373, 1999.

\bibitem{ipm:SWright7}
S.~J. Wright and D.~Ralph.
\newblock A superlinear infeasible--interior--point algorithm for monotone
  nonlinear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 21:815--838, 1996.

\bibitem{ipm:SWright9}
S.~J. Wright and Y.~Zhang.
\newblock A superquadratic infeasible--interior--point method for linear
  complementarity problems.
\newblock {\em Mathematical Programming}, 73:269--289, 1996.

\bibitem{ipm:Wu4}
F.~Wu, S.~Q. Wu, and Y.~Ye.
\newblock Convergence of the {$O(\sqrt{n}\,L)$}--iteration homogeneous and
  self--dual linear programming algorithm.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1992.

\bibitem{ipm:Wu7}
F.~Wu, S.~Q. Wu, and Y.~Ye.
\newblock On quadratic convergence of the homogeneous and self--dual linear
  programming algorithm.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1993.

\bibitem{ipm:Wu8}
J.~H. Wu.
\newblock Interior point algorithm for some monotone variational inequality
  problems.
\newblock {Preprint}, Center for Research on Transportation, University of
  Montreal, Montreal, Quebec, Canada, 1994.

\bibitem{ipm:Wu9}
J.~H. Wu.
\newblock Modified primal path--following scheme for the monotone variational
  inequality problem.
\newblock {\em Journal of Optimization Theory and Applications}, 95:189--208,
  1997.

\bibitem{ipm:Wu6}
S.-P. Wu, S.~Boyd, and L.~Vandenberghe.
\newblock {FIR} filter design via semidefinite programming and spectral
  factorization.
\newblock {\em Proceedings of the 35th IEEE Conference on Decision and
  Control}, 1/4:271--276, 1996.

\bibitem{ipm:Wu1}
S.~Q. Wu and F.~Wu.
\newblock New algorithms for linear programming.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
  8(1):18--26, 1992.

\bibitem{ipm:Wu2}
S.~Q. Wu and F.~Wu.
\newblock A direct ellipsoid method for linear programming.
\newblock {\em Bulletin of the Australian Matehmatical Society}, 47(1):73--78,
  1993.

\bibitem{ipm:Wu3}
S.~Q. Wu and F.~Wu.
\newblock Rank--one techniques in log--barrier function methods for linear
  programming.
\newblock {\em Journal of Optimization Theory and Applications}, 82:405--413,
  1994.

\bibitem{ipm:Wu5}
Y.-C. Wu, A.~S. Debs, and R.~E. Marsten.
\newblock A direct nonlinear predictor--corrector primal--dual interior point
  approach to optimal power flows.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:876--883, 1994.
\newblock See also\,: {\em Proceedings of the Power Industry Computer
  Application Conference 1993, 138--}.

\bibitem{ipm:Xu5}
C.-X. Xu.
\newblock Interior point algorithms for linear complementarity patterns.
\newblock {\em Journal on Numerical Methods and Computer Applications},
  16:109--118, 1995.
\newblock (In Chinese).

\bibitem{ipm:Xu9}
S.~R. Xu.
\newblock The global linear convergence of an infeasible non--interior
  path--following algorithm for complementarity problems with uniform
  {P}--functions.
\newblock {Technical Report}, Department of Mathematics, University of
  Washington, Seattle, WA~98195, USA, December 1996.

\bibitem{ipm:Xu10}
S.~R. Xu and J.~V. Burke.
\newblock A polynomial time interior--point path following algorithm for {LCP}
  based on {Chen--Harker--Kanzow} smoothing techniques.
\newblock {Technical Report}, Department of Mathematics, University of
  Washington, Seattle, WA~98195, USA, September 1996.

\bibitem{ipm:Xu3}
S.~R. Xu and D.~Gong.
\newblock An interior point method for solving linear programming with hybrid
  linear constraints.
\newblock {\em Acta Scientarium Naturalium Universitatis Sunyatseni},
  31(4):19--25, 1992.
\newblock (In Chinese).

\bibitem{ipm:Xu1}
S.~R. Xu, H.~B. Yao, and Y.~Q. Chen.
\newblock An improved {Karmarkar} algorithm for linear programming and its
  numerical tests.
\newblock {\em Mathematica Applicata}, 5(1):14--21, 1992.
\newblock (In Chinese, English summary).

\bibitem{ipm:Xu11}
X.~Xu.
\newblock An infeasible interior--point algorithm for solving primal and dual
  geometric programs.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1994.

\bibitem{ipm:Xu6}
X.~J. Xu.
\newblock {\em Interior point method for linear programming\,: {Theory} and
  practice}.
\newblock PhD thesis, Institute of System Science, Academica Sinica, Beijing,
  China, 1991.

\bibitem{ipm:Xu8}
X.~J. Xu.
\newblock On the implementation of a homogeneous and self--dual linear
  programming algorithm.
\newblock {Technical Report}, College of Business Administration, University of
  Iowa, Iowa City, IA~52242, USA, 1994.

\bibitem{ipm:Xu7}
X.~J. Xu.
\newblock An $o(\sqrt{n}l)$--iteration large--step infeasible path--following
  algorithm for linear programming.
\newblock {Technical Report}, College of Business Administration, University of
  Iowa, Iowa City, IA~52242, USA, August 1994.

\bibitem{ipm:Xu2}
X.~J. Xu, P.-F. Hung, and Y.~Ye.
\newblock A simplified homogeneous and self--dual linear programming algorithm
  and its implementation.
\newblock {\em Annals of Operations Research}, 62:151--171, 1996.

\bibitem{ipm:Xu4}
X.~J. Xu and Y.~Ye.
\newblock A generalized homogeneous and self--dual algorithm for linear
  programming.
\newblock {\em Operations Research Letters}, 17:181--190, 1995.

\bibitem{ipm:Xuan1}
Z.~C. Xuan, X.~S. Li, and Y.~K. Sui.
\newblock An interior point method for solving surrogate dual problems in
  quadratic programming.
\newblock {\em Journal of the Dalian University of Technology}, 37:520--522,
  1997.
\newblock (In Chinese, English summary).

\bibitem{ipm:Xue1}
G.~Xue and Y.~Ye.
\newblock An efficient algorithm for minimizing a sum of {Euclidean} norms with
  applications.
\newblock {University of Vermont Research Report} CSEE/95/06--01, Department of
  Computer Science and Electrical Engineering, The University of Vermont,
  Burlington, VT~05405--0156, USA, June 1995.

\bibitem{ipm:Xue2}
G.~Xue and Y.~Ye.
\newblock An efficient algorithm for minimizing a sum of {P--norms}.
\newblock {Working Paper}, Department of Computer Science and Electrical
  Engineering, The University of Vermont, Burlington, VT~05405--0156, USA,
  August 1997.

\bibitem{ipm:Yabe1}
H.~Yabe and H.~Yamashita.
\newblock The speed of local convergence of a primal--dual interior point
  method that uses a quasi--{Newton} method.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku (Proceedings
  of the Conference of the State of the Art of Scientific Computing and its
  Prospects, Kyoto, 1993)}, 880:211--219, 1994.
\newblock (In Japanese).

\bibitem{ipm:Yabe2}
H.~Yabe and H.~Yamashita.
\newblock Q--superlinear convergence of primal--dual interior point
  quasi--{Newton} methods for constrained optimization.
\newblock {\em Journal of the Operations Research Society of Japan},
  40:415--436, 1997.

\bibitem{ipm:Yamakawa1}
E.~Yamakawa, Y.~Matrsubara, and M.~Fukushima.
\newblock A parallel primal--dual interior point method for multicommodity flow
  problems with quadratic costs.
\newblock {\em Journal of the Operations Research Society of Japan},
  39:566--591, 1996.
\newblock (In Japanese).

\bibitem{ipm:Yamashita1}
H.~Yamashita.
\newblock A polynomially and quadratically convergent method for linear
  programming.
\newblock {Working Paper}, Mathematical Systems Institute, Inc., Shinjuku,
  Tokyo, Japan, 1986.

\bibitem{ipm:Yamashita2}
H.~Yamashita.
\newblock A class of primal dual method for constrained optimization.
\newblock {Working Paper}, Mathematical Systems Institute, Inc., Tokyo, Japan,
  1991.

\bibitem{ipm:Yamashita5}
H.~Yamashita.
\newblock A globally convergent primal--dual interior point method for
  constrained optimization.
\newblock {\em Optimization Methods and Software}, 10:443--469, 1998.

\bibitem{ipm:Yamashita3}
H.~Yamashita and T.~Tanabe.
\newblock A primal--dual interior point method for linear and nonlinear
  programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Mathematical Systems Institute, Inc., Tokyo, Japan, May 1992.

\bibitem{ipm:Yamashita4}
H.~Yamashita and H.~Yabe.
\newblock Superlinear and quadratic convergence of some primal--dual interior
  point methods for constrained optimization.
\newblock {\em Mathematical Programming}, 75:377--397, 1996.

\bibitem{ipm:Yan1}
X.~Yan and V.~H. Quintana.
\newblock An efficient technique for solving dense row problems in
  security--constrained economic dispatch.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
  Symposium (Manhattan, KS, USA, September 1994)}, 2:568--574, 1994.

\bibitem{ipm:Yan3}
X.~Yan and V.~H. Quintana.
\newblock An infeasible interior--point algorithm for optimal power--flow
  problems.
\newblock {\em Electrical Power Systems Research}, 39:39--46, 1996.

\bibitem{ipm:Yan2}
X.~Yan and V.~H. Quintana.
\newblock An efficient predictor--corrector interior point algorithm for
  security--constrained economic dispatch.
\newblock {\em IEEE Transactions on Power Systems}, 12:803--810, 1997.

\bibitem{ipm:Yang4}
D.~Yang and S.~A. Zenios.
\newblock A scalable parallel interior point algorithm for stochastic linear
  programming and robust optimization.
\newblock {\em Computational Optimization and Applications}, 7:143--158, 1997.

\bibitem{ipm:Yang3}
E.~K. Yang and C.-H. Chou.
\newblock A method for solving least--squares problems arising from angular
  linear programs.
\newblock {\em Tamkang Journal of Mathematics}, 25:1--13, 1994.

\bibitem{ipm:Yang1}
E.~K. Yang and W.~S. Hwang.
\newblock An interior point method for dynamic {Leontief} type linear programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Institute of Applied Mathematics, Tsing Hua University, Hsinchu, 30043,
  People Republic of China, May 1990.
\newblock See Yang and Hwang \cite{ipm:Yang2}.

\bibitem{ipm:Yang2}
E.~K. Yang and W.~S. Hwang.
\newblock A barrier method for dynamic {Leontief} type linear programs.
\newblock {\em European Journal of Operational Research}, 60:296--305, 1992.

\bibitem{ipm:Yang6}
H.-H. Yang.
\newblock {\em Investigation of path--following algorithms for signomial
  geometric programming problems}.
\newblock PhD thesis, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1994.

\bibitem{ipm:Yang5}
H.-H. Yang and D.~L. Bricker.
\newblock Investigation of path--following algorithms for signomial geometric
  problems.
\newblock {\em European Journal of Operational Research}, 103:230--241, 1997.

\bibitem{ipm:Ye4}
Y.~Ye.
\newblock Barrier projection and sliding current objective method for linear
  programming.
\newblock {Talk held at the 12th Mathematical Programming Symposium, Boston,
  MA, USA}, Department of Engineering Economic Systems, Stanford University,
  Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Ye3}
Y.~Ye.
\newblock Cutting--objective and scaling methods---a polynomial algorithm for
  linear programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1985.
\newblock Submitted to {\em Mathematical Programming}.

\bibitem{ipm:Ye2}
Y.~Ye.
\newblock Cutting current--objective method in projective algorithm for linear
  programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, February 1985.

\bibitem{ipm:Ye46}
Y.~Ye.
\newblock K--projection and cutting--objective method for linear programming.
\newblock {Talk held at the 12th Mathematical Programming Symposium, Boston,
  MA, USA}, Department of Engineering Economic Systems, Stanford University,
  Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Ye1}
Y.~Ye.
\newblock A large group of projections for linear programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Ye40}
Y.~Ye.
\newblock A ''build--down'' simplex--{Karmarkar} method for linear programming.
\newblock {Technical Report}, Department of Engineering Economic Systems,
  Stanford University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye6}
Y.~Ye.
\newblock Dual approach of {Karmarkar's} algorithm and the ellipsoid method.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye7}
Y.~Ye.
\newblock Further development on the interior algorithm for convex quadratic
  programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye5}
Y.~Ye.
\newblock {\em Interior algorithms for linear, quadratic, and linearly
  constrained convex programming}.
\newblock PhD thesis, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye8}
Y.~Ye.
\newblock Karmarkar's algorithm and the ellipsoid method.
\newblock {\em Operations Research Letters}, 6:177--182, 1987.

\bibitem{ipm:Ye32}
Y.~Ye.
\newblock Bimatrix equilibrium points and potential functions.
\newblock {Working Paper} 88--16, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1988.

\bibitem{ipm:Ye10}
Y.~Ye.
\newblock The ''build--down'' scheme for path--following algorithms.
\newblock {Technical Report}, Integrated Systems Inc., Santa Clara, CA, USA,
  1988.

\bibitem{ipm:Ye11}
Y.~Ye.
\newblock A class of potential functions for linear programming.
\newblock {Management Science Working Paper} 88--13, Department of Management
  Science, University of Iowa, Iowa City, IA~52242, USA, 1988.

\bibitem{ipm:Ye38}
Y.~Ye.
\newblock On the interior algorithms for nonconvex quadratic programming.
\newblock {Manuscript}, Integrated Systems, Inc., Santa Clara, CA, USA, 1988.

\bibitem{ipm:Ye33}
Y.~Ye.
\newblock A combinatorial property of analytic centers of polytopes.
\newblock {Manuscript}, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye13}
Y.~Ye.
\newblock Eliminating columns and rows in potential reduction and
  path--following algorithms for linear programming.
\newblock {Working Paper Series} 89--7, Department of Management Science,
  University of Iowa, Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye14}
Y.~Ye.
\newblock An extension of {Karmarkar's} algorithm and the trust region method
  for quadratic programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 49--64. Springer Verlag, New York,
  1989.

\bibitem{ipm:Ye31}
Y.~Ye.
\newblock Further developments in potential reduction algorithm.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye28}
Y.~Ye.
\newblock Line searches in potential reduction algorithm for linear
  programming.
\newblock Manuscript, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye12}
Y.~Ye.
\newblock Potential functions and polytopes.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, October 1989.

\bibitem{ipm:Ye34}
Y.~Ye.
\newblock Anticipated behavior of affine scaling algorithms for linear
  programming.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ye16}
Y.~Ye.
\newblock A ''build--down'' scheme for linear programming.
\newblock {\em Mathematical Programming}, 46:61--72, 1990.

\bibitem{ipm:Ye17}
Y.~Ye.
\newblock A class of projective transformations for linear programming.
\newblock {\em SIAM Journal on Computing}, 19:457--466, 1990.

\bibitem{ipm:Ye19}
Y.~Ye.
\newblock Complexity analysis on {Karmarkar's} algorithm.
\newblock {Manuscript}, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ye26}
Y.~Ye.
\newblock Interior point algorithms for global optimization.
\newblock {\em Annals of Operations Research}, 25:59--74, 1990.

\bibitem{ipm:Ye39}
Y.~Ye.
\newblock An {$O(n^{3}L)$} potential reduction algorithm for linear
  programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 77--88. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Ye48}
Y.~Ye.
\newblock The potential algorithm for linear complementarity problems.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ye18}
Y.~Ye.
\newblock Recovering optimal basic variables in {Karmarkar's} polynomial
  algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 15:564--572, 1990.

\bibitem{ipm:Ye15}
Y.~Ye.
\newblock Comparative analysis of affine scaling algorithms based on
  simplifying assumptions.
\newblock {\em Mathematical Programming}, 52:405--414, 1991.

\bibitem{ipm:Ye50}
Y.~Ye.
\newblock Improving the asymptotic convergence of interior--point algorithms
  for linear programming.
\newblock {Working Paper} 91--15, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.

\bibitem{ipm:Ye27}
Y.~Ye.
\newblock Interior point algorithms for quadratic programming.
\newblock In S.~Kumar, editor, {\em Recent Developments in Mathematical
  Programming}, pages 237--261. Gordon~\& Beach Scientific Publishers,
  Philadelphia, PA, USA, 1991.

\bibitem{ipm:Ye53}
Y.~Ye.
\newblock A low complexity combined {phase\,I\,--\,phase\,II} potential
  reduction algorithm for linear programming.
\newblock {Working Paper} 91--1, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.

\bibitem{ipm:Ye52}
Y.~Ye.
\newblock On the $q$--order of convergence of interior--point algorithms for
  linear programming.
\newblock {Working Paper} 91--17, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.
\newblock Also published in {\em W. Fang (ed.), Proceedings of the 1992
  Symposium on Applied Mathematics, Institute of Applied Mathematics, Chinese
  Academy of Sciences, 1992, pp. 534--543}.

\bibitem{ipm:Ye9}
Y.~Ye.
\newblock An ${O(n^{3}L)}$ potential reduction algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 50:239--258, 1991.

\bibitem{ipm:Ye49}
Y.~Ye.
\newblock Extensions of the potential reduction algorithm for linear
  programming.
\newblock {\em Journal of Optimization Theory and Applications},
  72(3):487--498, 1992.

\bibitem{ipm:Ye25}
Y.~Ye.
\newblock A further result on the potential reduction algorithm for the
  {$P$}--matrix linear complementarity problem.
\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
  Computing}, pages 310--316. North Holland, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:Ye29}
Y.~Ye.
\newblock On an affine scaling algorithm for nonconvex quadratic programming.
\newblock {\em Mathematical Programming}, 52:285--300, 1992.

\bibitem{ipm:Ye35}
Y.~Ye.
\newblock On the finite convergence of interior--point algorithms for linear
  programming.
\newblock {\em Mathematical Programming}, 57:325--335, 1992.

\bibitem{ipm:Ye41}
Y.~Ye.
\newblock A potential reduction algorithm allowing column generation.
\newblock {\em SIAM Journal on Optimization}, 2:7--20, 1992.

\bibitem{ipm:Ye30}
Y.~Ye.
\newblock A fully polynomial--time approximation algorithm for computing a
  stationary point of the generalized linear complementarity problem.
\newblock {\em Mathematics of Operations Research}, 18:334--345, 1993.

\bibitem{ipm:Ye45}
Y.~Ye.
\newblock Toward probabilistic analysis of interior--point algorithms for
  linear programming.
\newblock {\em Mathematics of Operations Research}, 19:38--52, 1994.

\bibitem{ipm:Ye54}
Y.~Ye.
\newblock On the {von Neumann} economic growth problem.
\newblock {\em Mathematics of Operations Research}, 20:617--633, 1995.

\bibitem{ipm:Ye59}
Y.~Ye.
\newblock Convergence behavior of the central path homogeneous and self--dual
  cones.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1996.

\bibitem{ipm:Ye61}
Y.~Ye.
\newblock How partial knowledge helps to solve linear programs.
\newblock {\em Journal of Complexity}, 12:480--491, 1996.

\bibitem{ipm:Ye64}
Y.~Ye.
\newblock Approximating quadratic optimization with linear and boolean
  constraints.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, August 1997.

\bibitem{ipm:Ye63}
Y.~Ye.
\newblock Approximating quadratic programming with bound constraints.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, March 1997.

\bibitem{ipm:Ye56}
Y.~Ye.
\newblock Complexity analysis of the analytic center cutting plane method that
  uses multiple cuts.
\newblock {\em Mathematical Programming}, 78:85--104, 1997.

\bibitem{ipm:Ye57}
Y.~Ye.
\newblock {\em {Interior--Point Algorithms\,: Theory and Practice}}.
\newblock John Wiley\,\&\, Sons, New York, USA, 1997.

\bibitem{ipm:Ye60}
Y.~Ye.
\newblock On homogeneous and self--dual algorithms for {LCP}.
\newblock {\em Mathematical Programming}, 76:211--221, 1997.

\bibitem{ipm:Ye65}
Y.~Ye.
\newblock Approximating global quadratic optimization with convex quadratic
  constraints.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, July 1998.

\bibitem{ipm:Ye58}
Y.~Ye.
\newblock On the complexity of approximating a {KKT} point of quadratic
  programming.
\newblock {\em Mathematical Programming}, 80:195--211, 1998.

\bibitem{ipm:Ye62}
Y.~Ye.
\newblock Approximating quadratic programming with quadratic constraints.
\newblock {\em Mathematical Programming}, 84:219--226, 1999.

\bibitem{ipm:Ye51}
Y.~Ye and K.~M. Anstreicher.
\newblock On quadratic and ${O(\sqrt{n} L)}$ convergence of a
  predictor--corrector algorithm for {LCP}.
\newblock {\em Mathematical Programming}, 62:537--551, 1993.

\bibitem{ipm:Ye36}
Y.~Ye and S.~S. Chiu.
\newblock Recovering the shadow price in projection methods for linear
  programming.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1985.

\bibitem{ipm:Ye43}
Y.~Ye, O.~G{\"u}ler, R.~A. Tapia, and Y.~Zhang.
\newblock A quadratically convergent ${O(\sqrt{n}L)}$--iteration algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 59:151--162, 1993.

\bibitem{ipm:Ye47}
Y.~Ye and J.~A. Kaliski.
\newblock Further results on build--up approaches for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in, Anaheim, CA,
  USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, November 1991.

\bibitem{ipm:Ye20}
Y.~Ye and M.~Kojima.
\newblock Recovering optimal dual solutions in {Karmarkar's} polynomial
  algorithm for linear programming.
\newblock {\em Mathematical Programming}, 39:305--317, 1987.

\bibitem{ipm:Ye42}
Y.~Ye, K.~O. Kortanek, J.~A. Kaliski, and S.~Huang.
\newblock Near--boundary behavior of primal--dual potential reduction
  algorithms for linear programming.
\newblock {\em Mathematical Programming}, 58:243--255, 1993.

\bibitem{ipm:Ye21}
Y.~Ye and P.~M. Pardalos.
\newblock A class of linear complementarity problems solvable in polynomial
  time.
\newblock {\em Linear Algebra and Its Applications}, 152:3--17, 1991.

\bibitem{ipm:Ye37}
Y.~Ye and F.~A. Potra.
\newblock An interior--point algorithm for solving entropy optimization
  problems with globally linear and locally quadratic convergence rate.
\newblock {Working Paper Series} 90--22, Department of Management Science,
  University of Iowa, Iowa City, IA~52242, USA, 1990.
\newblock Same as Potra and Ye \cite{ipm:Potra5}.

\bibitem{ipm:Ye44}
Y.~Ye, R.~A. Tapia, and Y.~Zhang.
\newblock A superlinearly convergent ${O(\sqrt{n}L)}$--iteration algorithm for
  linear programming.
\newblock {Technical Report} TR--91--22, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Ye22}
Y.~Ye and M.~J. Todd.
\newblock Containing and shrinking ellipsoids in the path--following algorithm.
\newblock {\em Mathematical Programming}, 47:1--10, 1990.

\bibitem{ipm:Ye55}
Y.~Ye, M.~J. Todd, and S.~Mizuno.
\newblock An {$O(\sqrt{n} L)$}--iteration homogeneous and self--dual linear
  programming algorithm.
\newblock {\em Mathematics of Operations Research}, 19:53--67, 1994.

\bibitem{ipm:Ye23}
Y.~Ye and E.~Tse.
\newblock A polynomial--time algorithm for convex quadratic programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1986.

\bibitem{ipm:Ye24}
Y.~Ye and E.~Tse.
\newblock An extension of {Karmarkar's} projective algorithm for convex
  quadratic programming.
\newblock {\em Mathematical Programming}, 44:157--179, 1989.

\bibitem{ipm:Yeh1}
Q.~J. Yeh.
\newblock {\em A reduced dual affine scaling algorithm for solving assignment
  and transportation problems}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Research, Columbia University, New York, NY~10027, USA, 1989.

\bibitem{ipm:Yen1}
S.~D. Yen and W.~S. Levine.
\newblock Mixed {$H_{2H}$} infinity optimization\,: {A BMI} solution.
\newblock {\em Proceedings of the 1997 36th IEEE Conference on Decision and
  Control}, Part\,1/5:460--465, 1997.

\bibitem{ipm:Yoshise1}
A.~Yoshise.
\newblock An optimization method for convex programming problems -- the
  interior point method and analytical center.
\newblock {\em Systems Control and Informations}, 38:155--160, 1994.
\newblock (In Japanese).

\bibitem{ipm:Yoshise2}
A.~Yoshise.
\newblock Complementarity problems.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 297--367. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Yuguo1}
H.~Yuguo, L.~Guangyi, and Y.~Erkeng.
\newblock A new {OPF} (optimal power flow) algorithm based on {Karmarkar's}
  interior point method.
\newblock {\em Proceedings of the Chinese Society of Electrical Engineering},
  16:409--412, 1996.
\newblock (In Chinese).

\bibitem{ipm:Yun1}
Z.~G. Yun.
\newblock High--order large--step interior--point algorithms for linear
  complementarity problems.
\newblock {Research Report} 650, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1994.
\newblock Identical to Zhao\,\cite{ipm:Zhao9}.

\bibitem{ipm:Yun2}
Z.~G. Yun and Z.~W. Liu.
\newblock A line--search method for {Lagrangian} relexation ascent algorithms.
\newblock {Research Report} 644, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1994.
\newblock Identical to Zhao and Liu\,\cite{ipm:Zhao10}.

\bibitem{ipm:Zaijan1}
D.~Zaijan.
\newblock A modified {Karmarkar's} algorithm.
\newblock {\em Applied Mathematics---A Journal of Chinese Universities},
  3:41--56, 1988.

\bibitem{ipm:Zaporozhan1}
D.~I. Zaporozhan.
\newblock Exact shifts of the constraints in methods of centers.
\newblock {\em Akademiya Nauk Respubliki Moldova Izvestiya Matematika}, pages
  72--86, 100, 103, 1993.

\bibitem{ipm:Zenios1}
S.~A. Zenios and R.~Qi.
\newblock Data--level parallel computing with interior point algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Decision Sciences, The Wharton School, University of
  Pennsylvania, Philadelphia, PA~19104, USA, April 1992.
\newblock See Eckstein et al.\ \cite{ipm:Eckstein1}.

\bibitem{ipm:Zenios2}
S.~A. Zenios and D.~Yang.
\newblock Massively parallel solution of robust optimization programs via
  interior point algorithms.
\newblock {Talk held at the INFORMS Joint National Meeting in Los Angeles, CA,
  USA}, Department of Decision Sciences, The Wharton School, University of
  Pennsylvania, Philadelphia, PA~19104, USA, April 1995.

\bibitem{ipm:Zhadan1}
V.~G. Zhadan.
\newblock Dual barrier--projection and barrier--{Newton} methods in linear
  programming.
\newblock In J.~Dolezal et~al., editor, {\em System Modelling and Optimization
  (Proceedings of the 17th IFIP Conference, Prague, Czech Republic, July
  1995)}, pages 501--509. Chapman \& Hall, London, Great Britain, 1996.

\bibitem{ipm:Zhang14}
D.~Zhang and Y.~Zhang.
\newblock An infeasible--interior--point algorithm with polynomiality and
  {$Q$}--subcubic convergence.
\newblock {Research Report} 93--13, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA, July
  1993.

\bibitem{ipm:Zhang17}
D.~Zhang and Y.~Zhang.
\newblock A {Mehrotra}--type predictor--corrector algorithm with polynomiality
  and {Q}--subquadratic convergence.
\newblock {\em Annals of Operations Research}, 62:131--150, 1996.

\bibitem{ipm:Zhang6}
J.~Z. Zhang.
\newblock The affine transformation method and the path following method for
  solving linear programming problems.
\newblock {\em Chinese Journal of Operations Research}, 8(2):25--34, 1989.
\newblock (In Chinese).

\bibitem{ipm:Zhang4}
S.~Zhang.
\newblock On the convergence property of {Iri--Imai's} method for linear
  programming.
\newblock {Technical Report} 8917/A, Economic Institute, Erasmus University,
  Rotterdam, The Netherlands, 1989.
\newblock See also Zhang \cite{ipm:SZhang1}.

\bibitem{ipm:SZhang1}
S.~Zhang.
\newblock The convergence property of the {Iri--Imai} algorithm for some smooth
  convex programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 82:121--138,
  1994.
\newblock See also Zhang \cite{ipm:Zhang4}.

\bibitem{ipm:SZhang2}
S.~Zhang and M.~Shi.
\newblock On the polynomiality of {Iri and Imai's} new algorithm for linear
  programming.
\newblock {\em Journal of Qinhua University}, 28:121--126, 1988.
\newblock (In Chinese).

\bibitem{ipm:Zhang21}
X.~Zhang and K.-C. Zhang.
\newblock A homotopy interior algorithm for posynomial geometric programming.
\newblock {\em Mathematica Numerica Sinica}, 18:225--232, 1996.
\newblock (In Chinese).

\bibitem{ipm:Zhang20}
X.~Zhang and J.~Zhou.
\newblock Interior point method for solving optimization problems.
\newblock {\em Proceedings of the International Conference on Intelligent
  Manufacturing (Wuhan, China, 1995)}, pages 149--155, 1995.

\bibitem{ipm:Zhang19}
X.~Zhang, J.~Zhou, and J.~Yu.
\newblock An optimization method based on a primal--dual interior point
  quadratic programming approach.
\newblock {\em Journal of the Huazhong University of Science and Technology},
  23(9):1--5, 1995.
\newblock (In Chinese).

\bibitem{ipm:Zhang5}
Y.~Zhang.
\newblock Super--linear convergence of interior point algorithms for a class of
  mathematical programming problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Mathematics \& Statistics, University of
  Maryland Baltimore County, Baltimore, MD~21228, USA, May 1991.

\bibitem{ipm:Zhang12}
Y.~Zhang.
\newblock A primal--dual interior point approach for computing the $\ell_{1}$
  and $\ell_{\infty}$ solutions of overdetermined linear systems.
\newblock {\em Journal of Optimization Theory and Applications},
  77(2):323--341, 1993.

\bibitem{ipm:Zhang23}
Y.~Zhang.
\newblock {LIPSOL -- A MATLAB} toolkit for linear programming interior--point
  solvers.
\newblock {Technical Report}, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA,
  1994.
\newblock See also Zhang \cite{ipm:Zhang23}.

\bibitem{ipm:Zhang11}
Y.~Zhang.
\newblock On the convergence of a class of infeasible interior--point methods
  for the horizontal linear complementarity problem.
\newblock {\em SIAM Journal on Optimization}, 4:208--227, 1994.

\bibitem{ipm:Zhang22}
Y.~Zhang.
\newblock User's guide to {LIPSOL}.
\newblock {Technical Report}, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA, July
  1995.
\newblock See also Zhang \cite{ipm:Zhang24}.

\bibitem{ipm:Zhang18}
Y.~Zhang.
\newblock Solving large--scale linear programs by interior--point methods under
  the {MATLAB} environment.
\newblock {Technical Report} 96--01, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA,
  March 1996.

\bibitem{ipm:Zhang16}
Y.~Zhang.
\newblock On extending primal--dual interior--point algorithms from linear
  programming to semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:365--386, 1998.

\bibitem{ipm:Zhang10}
Y.~Zhang and A.~S. El-Bakry.
\newblock A modified predictor--corrector algorithm for locating weighted
  centers in linear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 80:319--331,
  1994.

\bibitem{ipm:Zhang7}
Y.~Zhang and R.~A. Tapia.
\newblock A quadratically convergent polynomial primal--dual interior--point
  algorithm for linear programming.
\newblock {Technical Report} TR~90--40, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1990.
\newblock To appear in {\em SIAM Journal on Optimization 3 (1993)}.

\bibitem{ipm:Zhang9}
Y.~Zhang and R.~A. Tapia.
\newblock On the convergence of interior--point methods to the center of the
  solution set in linear programming.
\newblock {Technical Report} TR~91--30, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Zhang3}
Y.~Zhang and R.~A. Tapia.
\newblock A polynomial--time and superlinearly convergent interior point
  algorithm for linear programming.
\newblock {Technical Report}, Department of Mathematical Sciences, Rice
  University, Houston, TX~77251, USA, March 1991.
\newblock To appear in {\em SIAM Journal on Optimization, 1992}.

\bibitem{ipm:Zhang8}
Y.~Zhang and R.~A. Tapia.
\newblock Superlinear and quadratic convergence of primal--dual interior--point
  methods for linear programming revisited.
\newblock {\em Journal of Optimization Theory and Applications},
  73(2):229--242, 1992.

\bibitem{ipm:Zhang1}
Y.~Zhang, R.~A. Tapia, and J.~E. Dennis.
\newblock On the superlinear and quadratic convergence of primal--dual interior
  point linear programming algorithms.
\newblock {\em SIAM Journal on Optimization}, 2(2):304--324, 1992.

\bibitem{ipm:Zhang2}
Y.~Zhang, R.~A. Tapia, and F.~Potra.
\newblock On the superlinear convergence of interior point algorithms for a
  general class of problems.
\newblock {\em SIAM Journal on Optimization}, 3(2):413--422, 1993.

\bibitem{ipm:Zhang13}
Y.~Zhang and D.~Zhang.
\newblock Superlinear convergence of infeasible interior--point methods for
  linear programming.
\newblock {\em Mathematical Programming}, 66:361--377, 1994.

\bibitem{ipm:Zhang15}
Y.~Zhang and D.~Zhang.
\newblock On polynomiality of the {Mehrotra}--type predictor--corrector
  interior--point algorithm.
\newblock {\em Mathematical Programming}, 68:303--318, 1995.

\bibitem{ipm:Zhao6}
G.~Y. Zhao.
\newblock {\em Estimating the complexity of path--following methods in linear
  programming by curvature integrals along the central trajectory}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  1991.

\bibitem{ipm:Zhao11}
G.~Y. Zhao.
\newblock Large--step path--following primal--dual algorithms for linear
  programming.
\newblock {Research Report} 613, Department of Mathematics, National University
  of Singapore, Singapore~0511, March 1994.

\bibitem{ipm:Zhao9}
G.~Y. Zhao.
\newblock High--order large--step interior point algorithms for linear
  complementary problems.
\newblock {Research Report} 650, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1995.
\newblock Identical to Yun\,\cite{ipm:Yun1}.

\bibitem{ipm:Zhao7}
G.~Y. Zhao.
\newblock On the choice of parameters for power--series interior point
  algorithms in linear programming.
\newblock {\em Mathematical Programming}, 68:49--71, 1995.

\bibitem{ipm:Zhao15}
G.~Y. Zhao.
\newblock Interior point methods with decomposition for linear programs.
\newblock {Research Report} 686, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1996.

\bibitem{ipm:Zhao3}
G.~Y. Zhao.
\newblock Relationship between the curvature integral and the complexity of
  path--following methods in linear programming.
\newblock {\em SIAM Journal on Optimization}, 6:57--73, 1996.

\bibitem{ipm:Zhao13}
G.~Y. Zhao.
\newblock Log--barrier decomposition methods for solving two--stage stochastic
  programs.
\newblock {Research Report} 711, Department of Mathematics, National University
  of Singapore, Singapore~0511, June 1997.
\newblock Revised June 1998.

\bibitem{ipm:Zhao16}
G.~Y. Zhao.
\newblock Barrier function in the {Lagrangian} dual method for solving
  multi--stage stochastic nonlinear programs.
\newblock {Research Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, 1998.

\bibitem{ipm:Zhao12}
G.~Y. Zhao.
\newblock Interior point algorithms for linear complementarity problems based
  on large neighborhoods of the central path.
\newblock {\em SIAM Journal on Optimization}, 8:397--413, 1998.

\bibitem{ipm:Zhao10}
G.~Y. Zhao and Z.~W. Liu.
\newblock A line search method for {Lagrangian} relaxation ascent algorithms.
\newblock {Technical Report} 644, Department of Mathematics, National
  University of Singapore, Singapore~0511, 1995.
\newblock Identical to Yun and Liu\,\cite{ipm:Yun2}.

\bibitem{ipm:Zhao1}
G.~Y. Zhao and J.~Stoer.
\newblock Estimating the complexity of path--following methods for solving
  linear programs by curvature integrals.
\newblock {\em Applied Mathematics~{\&}~Optimization}, 27(1):85--103, 1993.

\bibitem{ipm:Zhao14}
G.~Y. Zhao and J.~Sun.
\newblock On the rate of local convergence of higher--order
  infeasible--path--following algorithms for {$P_{*}$--LCP with or without
  strictly complementary solutions}.
\newblock {Research Report} 698, Department of Mathematics, National University
  of Singapore, Singapore~0511, March 1997.

\bibitem{ipm:Zhao8}
G.~Y. Zhao, J.~Sun, and J.~Zhu.
\newblock A primal--dual affine scaling algorithm with necessary centering as a
  safeguard.
\newblock {\em Optimization}, 35:333--343, 1995.

\bibitem{ipm:Zhao5}
G.~Y. Zhao and J.~Zhu.
\newblock Analytical properties of the central trajectory in interior point
  methods.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 362--375. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Zhao4}
G.~Y. Zhao and J.~Zhu.
\newblock The curvature integral and the complexity of linear complementarity
  problems.
\newblock {\em Mathematical Programming}, 70:107--122, 1995.

\bibitem{ipm:Zhao2}
Y.~Zhao.
\newblock A classification of trajectory optimization algorithms.
\newblock {Technical Report} 91/115, Minnesota Supercomputer Institute,
  University of Minnesota, Minneapolis, MN~55415, USA, April 1991.

\bibitem{ipm:Zheng1}
Q.~Zheng.
\newblock On the complexity of linear programming problems.
\newblock {\em Chinese Journal of Operations Research}, 7(2):1--10, 1988.
\newblock (In Chinese).

\bibitem{ipm:Zhou1}
J.~Zhou, N.~Xu, and W.~Chen.
\newblock Discussion on {Karmarkar's} method for solving unstandard model.
\newblock {\em Journal of Southeastern University (Nanjing, PR China), English
  Edition}, 5(1):38--45, 1989.

\bibitem{ipm:Zhu2}
J.~Zhu.
\newblock A path following algorithm for a class of convex programming
  problems.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 36(4):539--377, 1992.

\bibitem{ipm:Zhu3}
J.~Zhu and S.~Huang.
\newblock On the convergence rate of the duality gap in a symmetric
  primal--dual potential reduction algorithm.
\newblock {\em Operations Research Letters}, 11:289--291, 1992.

\bibitem{ipm:Zhu1}
J.~Zhu and K.~O. Kortanek.
\newblock A polynomial path--following algorithm for linearly constrained
  convex programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, College of Business Administration, University of Iowa, Iowa City,
  IA~52240, USA, October 1990.

\bibitem{ipm:Zikan1}
K.~Zikan and R.~W. Cottle.
\newblock The box method for linear programming, {Part\,I\,: Basic} theory.
\newblock {Technical Report}, Systems Optimization Laboratory, Department of
  Operations Research, Stanford University, Stanford, CA~94305--4022, USA,
  1987.

\bibitem{ipm:Zikan2}
K.~Zikan and R.~W. Cottle.
\newblock The box method for linear programming, {Part\,II\,: Treatment} of
  problems in standard form with explicitly bounded variables.
\newblock {Technical Report}, Systems Optimization Laboratory, Department of
  Operations Research, Stanford University, Stanford, CA~94305--4022, USA,
  1987.

\bibitem{ipm:Zikan3}
K.~Zikan and R.~W. Cottle.
\newblock Solving linear programs with the box method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Systems Optimization Laboratory, Department of Operations Research,
  Stanford University, Stanford, CA~94305--4022, USA, April 1988.

\bibitem{ipm:Zimmermann1}
U.~Zimmermann.
\newblock On recent developments in linear programming.
\newblock In K.~H. Hoffmann, J.~B. Hiriat-Urruty, C.~Lemarechal, and J.~Zowe,
  editors, {\em Trends in Mathematical Optimization\,: Proceedings of the 4th
  French--German Conference on Optimization in Irsee, Germany, April 1986},
  volume~84 of {\em International Series of Numerical Mathematics}, pages
  353--390. Birkh{\"a}user Verlag, Basel, Switzerland, 1988.

\bibitem{ipm:Zimmermann2}
U.~Zimmermann.
\newblock Search directions for projective methods.
\newblock {Technical Report}, Technische Universit{\"a}t Braunschweig, Institut
  f{\"u}r Angewandte Mathematik, Abt.\ f{\"u}r Math.\ Optimierung,
  Pockelstr.~14, D--3300~Braunschweig, Germany, February 1989.

\bibitem{ipm:Zimmermann3}
U.~Zimmermann.
\newblock Search directions for a class of projective methods.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 34:353--379, 1990.

\bibitem{ipm:Zimmermann4}
U.~Zimmermann and C.~Wallacher.
\newblock An interior point method for flow problems.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Technische
  Universit{\"a}t Braunschweig, Institut f{\"u}r Angewandte Mathematik, Abt.\
  f{\"u}r Math.\ Optimierung, Pockelstr.~14, D--3300~Braunschweig, Germany,
  August 1990.
\newblock See also Wallacher and Zimmermann \cite{ipm:Wallacher1}.

\end{thebibliography}
