# =============================================================== # CHEBYQUAD FUNCTION (R. Fletcher, "Function Minimization Without # Evaluating Derivatives -- A Review", # Computer J. 8 (1965), pp. 163-168.) # =============================================================== param n > 0; var x {j in 1..n} := j/(n+1); var T {i in 0..n, j in 1..n} = if (i = 0) then 1 else if (i = 1) then 2*x[j] - 1 else 2 * (2*x[j]-1) * T[i-1,j] - T[i-2,j]; # ======================= # Equation form (for nl2) # ======================= eqn {i in 1..n}: (1/n) * sum {j in 1..n} T[i,j] = if (i mod 2 = 0) then 1/(1-i^2) else 0; # ======================== # Objective form (for mng) # ======================== minimize ssq: 0.5*sum{i in 1..n} ((1/n) * sum {j in 1..n} T[i,j] - if (i mod 2 = 0) then 1/(1-i^2))^2; data; param n := 3;