Description
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
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds928.gms
$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';