Small Synthesis Example
minco
Couenne
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.