Description
Test problem 9.2.6 in Handbook of Test Problems in Local and Global Optimization Test problem 9.1.5 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. Bard J F, Some properties of the bilevel programming problem, Journal of Optimization Theory and Applications, v.68 n.2, p.371-378, Feb. 1991 Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds915.gms
$title Princeton Bilevel Optimization Example 9.1.5 (FLDS915,SEQ=31)
$onText
Test problem 9.2.6 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.5 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.
Bard J F, Some properties of the bilevel programming problem, Journal of
Optimization Theory and Applications, v.68 n.2, p.371-378, Feb. 1991
Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
$offText
*Solution of problem 9.1.5 on the web
scalar x_l / 1 /
y1_l / 0 /
y2_l / 0 /
tol / 1e-6 /;
variables z, z_in; positive variable x, y1, y2;
equations ob, ob_in, c1, c2, c3;
ob.. - x + 10*y1 - y2 =e= z;
ob_in .. - y1 - y2 =e= z_in;
c1.. x + y1 =l= 1;
c2.. x + y2 =l= 1;
c3.. y1 + y2 =l= 1;
model bilevel / all /;
$echo bilevel x min z_in y1 y2 ob_in c1 c2 c3 > "%emp.info%"
*Start from reported solution
x.l = x_l ;
y1.l = y1_l;
y2.l = y2_l;
solve bilevel using EMP minimizing z;
abort$( (abs( x.l - x_l) > tol)
or (abs(y1.l - y1_l) > tol)
or (abs(y2.l - y2_l) > tol) ) 'Deviated from reported solution';