$title Princeton Bilevel Optimization Example 9.2.8 (FLDS928,SEQ=43)

$onText

  Test problem 9.3.9 in Handbook of Test Problems in Local and Global Optimization
  Test problem 9.2.8 on http://titan.princeton.edu/TestProblems/chapter9.html

References:

Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding,
S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in
Local and Global Optimization. Kluwer Academic Publishers, 1999

Yezza, A. (1996). First-order necessary optimality conditions for general bilevel
programming problems. Journal of Optimization Theory and Applications, 89:189-219.

Contributor: Jan-H. Jagla, January 2010

$offText

*Solution of problem 9.2.8 on the web
scalar  x_l / 0.25 /
        y_l /    0 /
        tol / 1e-6 /;

variables z, z_in, y; positive variable x;
equations ob, c0, c1, c2;

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

c0..         y - 4*x*y     =e= z_in;
c1..     -   y             =l=    0;
c2..         y             =l=    1;

model bilevel / all /;

$echo bilevel x max z_in y c0 c1 c2 > "%emp.info%"

*Start from reported solution
x.l = x_l;
y.l = y_l;

solve bilevel using EMP minimizing z;

abort$(   (abs(x.l - x_l) > tol)
       or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';