* Test problem 9.3.9 in the Test Collection Book
* Test problem 9.2.8 in the web page
* Test problem from Yezza 96
* Bilinear Inner Objective

SET i /1*2/;

PARAMETER bigu;

bigu = 40;

VARIABLES

z;

POSITIVE VARIABLES

x, y, s(i), lb(i);

EQUATIONS

ob, c1, c2, cs(i), kt1;

* Outer Objective function

ob.. -4*x*y + 3*y + 2*x + 1 =e= z;

* Inner Problem Constraints

c1..  -y + s('1') =e= 0;

c2..   y + s('2') =e= 1;

* KKT conditions for the inner problem optimum

kt1..  -(1 - 4*x) - lb('1') + lb('2') =e= 0;

* Complementarity Constraints

cs(i).. lb(i)*s(i) =e= 0;

x.up     = 1;
s.up(i)  = 20;
lb.up(i) = 0;

MODEL BARD91/ALL/;

SOLVE BARD91 USING NLP MINIMIZING z;