* Test problem 9.3.2 in the Test Collection Book * Test problem 9.2.1 in the web page * Test problem from Shimizu etal 1997 SET i /1*4/; PARAMETER bigu; bigu = 40; VARIABLES z; POSITIVE VARIABLES x, y, s(i), lb(i); EQUATIONS ob, c1, c2, c3, c4, cs(i), kt1; * Outer Objective function ob.. (x - 5)*(x-5) + (2*y + 1)*(2*y + 1) =e= z; * Inner Problem Constraints c1.. -3*x + y + s('1') =e= -3; c2.. x - 0.5*y + s('2') =e= 4; c3.. x + y + s('3') =e= 7; c4.. - y + s('4') =e= 0; * KKT conditions for the inner problem optimum kt1.. 2*(y-1) - 1.5*x + lb('1') - 0.5*lb('2') + lb('3') - lb('4') =e= 0; * Complementarity Constraints cs(i).. s(i)*lb(i) =e= 0; s.up(i) = 20; lb.up(i) = 20; MODEL SHI/ALL/; SOLVE SHI USING NLP MINIMIZING z;