Small Synthesis Example minco MINLP AMPL short = 0, <= u[i]; var y {J} >= 0, <= 1, binary; minimize Obj: 5*y[1] + 8*y[2] + 6*y[3] + 10*y[4] + 6*y[5] + 7*y[6] + 4*y[7] + 5*y[8] - 10*x[1] - 15*x[2] + 15*x[3] + 80*x[4] + 25*x[5] + 35*x[6] - 40*x[7] + 15*x[8] - 35*x[9] + exp(x[1]) + exp(0.833333*x[2]) - 65*log(x[3]+x[4]+1) - 90*log(x[5]+1) - 80*log(x[6]+1) + 120; s.t. c1: - 1.5*log(x[5]+1) - log(x[6]+1) - x[8] <= 0; c2: - log(x[3]+x[4]+1) <= 0; c3: - x[1] - x[2] + x[3] + 2*x[4] + 0.8*x[5] + 0.8*x[6] - 0.5*x[7] - x[8] - 2*x[9] <= 0; c4: - x[1] - x[2] + 2*x[4] + 0.8*x[5] + 0.8*x[6] - 2*x[7] - x[8] - 2*x[9] <= 0; c5: - 2*x[4] - 0.8*x[5] - 0.8*x[6] + 2*x[7] + x[8] + 2*x[9] <= 0; c6: - 0.8*x[5] - 0.8*x[6] + x[8] <= 0; c7: - x[4] + x[7] + x[9] <= 0; c8: - 0.4*x[5] - 0.4*x[6] + 1.5*x[8] <= 0; c9: 0.16*x[5] + 0.16*x[6] - 1.2*x[8] <= 0; c10: x[3] - 0.8*x[4] <= 0; c11: - x[3] + 0.4*x[4] <= 0; c12: exp(x[1]) - 10*y[1] <= 1; c13: exp(0.833333*x[2]) - 10*y[2] <= 1; c14: x[7] - 10*y[3] <= 0; c15: 0.8*x[5] + 0.8*x[6] - 10*y[4] <= 0; c16: 2*x[4] - 2*x[7] - 2*x[9] - 10*y[5] <= 0; c17: x[5] - 10*y[6] <= 0; c18: x[6] - 10*y[7] <= 0; c19: x[3] + x[4] - 10*y[8] <= 0; c20: y[1] + y[2] = 1; c21: y[4] + y[5] <= 1; c22: - y[4] + y[6] + y[7] = 0; c23: y[3] - y[8] <= 0; ]]> solve; display _varname, _var; Source: Test problem 1 (Synthesis of processing system) in M. Duran and I.E. Grossmann, "An outer approximation algorithm for a class of mixed integer nonlinear programs", Mathematical Programming 36, pp. 307-339, 1986.