* MINLP literature problem * Berman and Ashrafi, 1993. * NOTE: The problem has been reformulated so that no binary * variables appear in nonlinear terms as this cannot be * handled by GAMS solvers. VARIABLES x1 x2 x3 y1 y2 y3 y4 y5 y6 y7 y8 objval objective function variable; FREE VARIABLES objval; BINARY VARIABLE y1; BINARY VARIABLE y2; BINARY VARIABLE y3; BINARY VARIABLE y4; BINARY VARIABLE y5; BINARY VARIABLE y6; BINARY VARIABLE y7; BINARY VARIABLE y8; EQUATIONS f Objective function h1 h2 h3 g1 g2 g3 g4 ; f .. objval =e=((-x1)*x2)*x3; g1 .. -y1-y2-y3 =l= -1; g2 .. -y4-y5-y6 =l= -1; g3 .. -y7-y8 =l= -1; g4 .. 3*y1+y2+2*y3+3*y4+2*y5+y6+3*y7+2*y8 =l= 10; h1 .. LOG(0.1)*y1+LOG(0.2)*y2+LOG(0.15)*y3-LOG(1-x1) =e= 0; h2 .. LOG(0.05)*y4+LOG(0.2)*y5+LOG(0.15)*y6-LOG(1-x2) =e= 0; h3 .. LOG(0.02)*y7+LOG(0.06)*y8-LOG(1-x3) =l= 0; * Bounds x1.LO = 0; x1.UP = 0.997; x2.LO = 0; x2.UP = 0.9985; x3.LO = 0; x3.UP = 0.9988; * Starting point (global solution) * x1.L = 0.97; x2.L = 0.9925; x3.L = 0.98; * y1.L = 0; y2.L = 1; y3.L = 1; y4.L = 1; * y5.L = 0; y6.L = 1; y7.L = 1; y8.L = 0; MODEL test /ALL/; SOLVE test USING MINLP MINIMIZING objval;