* Test problem 9.2.5 in the Test Collection Book
* Test problem 9.1.4 in the web page
* Test problem from Clark and Westerberg 1988


SET i /1*4/;

PARAMETER bigu;

bigu = 400;

VARIABLES

z;

POSITIVE VARIABLES

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

EQUATIONS

c1, c2, c3, c4, c5, cs1(i), kt1;

* Outer Objective function

c1..     x - 4*y =e= z;

* Inner Problem Constraints

c2..  -2*x +   y + s('1') =e= 0;

c3..   2*x + 5*y + s('2') =e= 108;

c4..   2*x - 3*y + s('3') =e= -4;

c5..         - y + s('4') =e= 0; 

* KKT conditions for the inner problem optimum

kt1..  lb('1') + 5*lb('2') - 3*lb('3') - lb('4') =e= -1;

* Complementarity Constraints

cs1(i).. lb(i)*s(i) =e= 0;

lb.up(i) = 200;
s.up(i)  = 200;

MODEL CKWG/ALL/;

SOLVE CKWG USING NLP MINIMIZING z;