* Test problem 9.3.10 in the Test Collection Book * Test problem 9.2.9 in the web page * Test problem from Bard 91 SET i /1*3/; PARAMETER bigu; bigu = 20; VARIABLES z; POSITIVE VARIABLES x, y1, y2, s(i), lb(i); BINARY VARIABLES yb(i); EQUATIONS ob, c1, c2, c3, cs1(i), cs2(i), kt1, kt2; * Outer Objective function ob.. x + y2 =e= z; * Inner Problem Constraints c1.. x - y1 - y2 + s('1') =e= -4; c2.. - y1 + s('2') =e= 0; c3.. - y2 + s('3') =e= 0; * KKT conditions for the inner problem optimum kt1.. - lb('1') - lb('2') =e= -2; kt2.. - lb('1') - lb('3') =e= -x; * Complementarity Constraints cs1(i).. lb(i) - bigu*yb(i) =l= 0; cs2(i).. s(i) - bigu*(1 - yb(i)) =l= 0; x.lo = 2; x.up = 4; MODEL BARD91/ALL/; SOLVE BARD91 USING MIP MINIMIZING z;