Description
Test problem 9.2.10 in Handbook of Test Problems in Local and Global Optimization Test problem 9.1.9 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. Visweswaran, V., C. Floudas, M. Ierapetritou, and E. Pistikopoulos, A Decomposition Based Global Optimization Approach for Solving Bilevel Linear and Nonlinear Quadratic Programs. In Floudas and Pardalos (eds.), State of the Art in Global Optimization: Computational Methods and Applications. Kluwer Academic Publishers, 1996. Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds919.gms
$title Princeton Bilevel Optimization Example 9.1.9 (FLDS919,SEQ=35)
$onText
Test problem 9.2.10 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.9 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.
Visweswaran, V., C. Floudas, M. Ierapetritou, and E. Pistikopoulos, A
Decomposition Based Global Optimization Approach for Solving Bilevel Linear and
Nonlinear Quadratic Programs. In Floudas and Pardalos (eds.), State of the Art
in Global Optimization: Computational Methods and Applications. Kluwer Academic
Publishers, 1996.
Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
$offText
*Solution of problem 9.1.9 on the web
scalar x_l,
y_l,
tol / 1e-6 /;
x_l = 8/9;
y_l = 20/9;
variables z; positive variable x, y;
equations ob, c2, c3, c4, c5, c6;
ob.. x + y =e= z;
c2.. -x - 0.5*y =l= -2;
c3.. -0.25*x + y =l= 2;
c4.. x + 0.5*y =l= 8;
c5.. x - 2*y =l= 2;
c6.. - y =l= 0;
model bilevel / all /;
$echo bilevel x max y c2 c3 c4 c5 c6 > "%emp.info%"
*Start from reported solution
x.l = x_l;
y.l = y_l;
solve bilevel using EMP minimizing z;
abort$( (abs(x.l - x_l) > tol)
or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';