bard3 problem mpec Knitro AMPL short = 0; var y{N} >= 0; # ... slack variables & multipliers var l{N} >= 0; minimize f: - x[1]^2 - 3*x[2] - 4*y[1] + y[2]^2; subject to nlncs: x[1]^2 + 2*x[2] <= 4; KKT1: 2*y[1] + l[1]*2 - l[2]*3 = 0; KKT2: -5 - l[1] + l[2]*4 = 0; lin_1: 0 <= x[1]^2 - 2*x[1] + x[2]^2 - 2*y[1] + y[2] + 3 complements l[1] >= 0; lin_2: 0 <= x[2] + 3*y[1] - 4*y[2] - 4 complements l[2] >= 0; ]]> solve; display _varname, _var; Knitro-AMPL sample submission