Description
Test problem 9.2.3 in Handbook of Test Problems in Local and Global Optimization Test problem 9.1.2 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. Liu, Y H, and Hart, S M, Characterizing an Optimal Solution to the Linear Bilevel Programming Problem. European Journal of Operational Research 79 (1994), 164-166. Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds912.gms
$title Princeton Bilevel Optimization Example 9.1.2 (FLDS912,SEQ=28)
$onText
Test problem 9.2.3 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.2 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.
Liu, Y H, and Hart, S M, Characterizing an Optimal Solution to the Linear Bilevel
Programming Problem. European Journal of Operational Research 79 (1994), 164-166.
Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
$offText
*Solution of problem 9.1.2 on the web
scalar x_l / 4 /
y_l / 4 /
tol / 1e-6 /;
variables z, z_in; positive variables x, y;
equation ob, c2, c3, c4, c5;
ob.. - x - 3*y =e= z;
c2.. - x + y =l= 3;
c3.. x + 2*y =l= 12;
c4.. 4*x - y =l= 12;
c5.. - y =l= 0;
model bilevel / all /;
$echo bilevel x min y c2 c3 c4 c5 > "%emp.info%"
*Start from reported solution
x.l = x_l;
y.l = y_l;
solve bilevel using EMP minimizing z;
abort$( (abs(x.l - x_l) > tol)
or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';