* Test problem 9.2.10 in the Test Collection Book * Test problem 9.1.9 in the web page * Test Problem from visweswaran-etal 1996 * Taken from Bard 1983 SET i /1*5/; PARAMETER bigu; bigu = 10; VARIABLES z; POSITIVE VARIABLES x, y, s(i), lb(i); BINARY VARIABLES yb(i); EQUATIONS c1, c2, c3, c4, c5, c6, cs1(i), cs2(i), kt1; * Outer Objective function c1.. x + y =e= z; * Inner Problem Constraints c2.. -x - 0.5*y + s('1') =e= -2; c3.. -0.25*x + y + s('2') =e= 2; c4.. x + 0.5*y + s('3') =e= 8; c5.. x - 2*y + s('4') =e= 2; c6.. - y + s('5') =e= 0; * KKT conditions for the inner problem optimum kt1.. -0.5*lb('1') + lb('2') + 0.5*lb('3') - 2*lb('4') - lb('5') =e= 1; * Complementarity Constraints cs1(i).. lb(i) - bigu*yb(i) =l= 0; cs2(i).. s(i) - bigu*(1 - yb(i)) =l= 0; MODEL BARDFALK/ALL/; SOLVE BARDFALK USING MIP MINIMIZING z;