* Test problem 9.2.8 in the Test Collection Book
* Test problem 9.1.8 in the web page
* Test problem from Bard and Falk 82
* Note the correct results are given here


SET i /1*5/;

PARAMETER bigu;

bigu = 10;

VARIABLES

z;

POSITIVE VARIABLES

x1, x2, y1, y2, s(i), lb(i);

EQUATIONS

ob, c0, c1, c2, c3, c4, cs1(i), kt1, kt2;

* Outer Objective function

ob.. - 2*x1 + x2 + 0.5*y1 =e= z;

* Outer constraint

c0..    x1 +   x2  =l= 2;

* Inner Problem Constraints

c1.. -2*x1 +   y1 - y2 + s('1')   =e= -2.5;

c2..    x1 - 3*x2 + y2 + s('2')   =e= 2;

c3..  -y1 + s('3') =e= 0;

c4..  -y2 + s('4') =e= 0;

* KKT conditions for the inner problem optimum

kt1..    lb('1') - lb('3') =e= 4;
kt2..    lb('1') + lb('2') - lb('4') =e= -1;

* Complementarity Constraints

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

MODEL BARD91/ALL/;

SOLVE BARD91 USING NLP MINIMIZING z;