* Test problem 9.3.7 in the Test Collection Book * Test problem 9.2.6 in the web page * Test problem from Falk and Liu 1995 * Original example from A.D. De Silva's dissertation 78 * Ouadratic Outer and Inner Objective - Nonlinear SET i /1*6/; PARAMETER bigu; bigu = 400; VARIABLES z; POSITIVE VARIABLES x1, x2, y1, y2, s(i), lb(i); EQUATIONS ob, c1, c2, c3, c4, cs(i), kt1, kt2; * Outer Objective function ob.. x1*x1 - 2*x1 + x2*x2 - 2*x2 + y1*y1 + y2*y2 =e= z; * Inner Problem Constraints c1.. 0.5 - y1 + s('1') =e= 0; c2.. 0.5 - y2 + s('2') =e= 0; c3.. y1 - 1.5 + s('3') =e= 0; c4.. y2 - 1.5 + s('4') =e= 0; * KKT conditions for the inner problem optimum kt1.. 2*(y1 - x1) - lb('1') + lb('3') =e= 0; kt2.. 2*(y2 - x2) - lb('2') + lb('4') =e= 0; * Complementarity Constraints cs(i).. s(i)*lb(i) =e= 0; s.up(i) = 200; lb.up(i) = 200; MODEL FALIU/ALL/; SOLVE FALIU USING NLP MINIMIZING z;