Description
Test problem 9.3.3 in Handbook of Test Problems in Local and Global Optimization Test problem 9.2.2 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 Aiyoshi, E and K. Shimizu (1981). Hierarchical Decentralized systems and its new solution by a Barrier Method. IEEE Trans. Systems, Man and Cybernetics, SMC-11, 444. Contributor: Jan-H. Jagla, January 2010
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds922.gms
$title Princeton Bilevel Optimization Example 9.2.2 (FLDS922,SEQ=37)
$onText
Test problem 9.3.3 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.2.2 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
Aiyoshi, E and K. Shimizu (1981). Hierarchical Decentralized systems and its
new solution by a Barrier Method. IEEE Trans. Systems, Man and Cybernetics,
SMC-11, 444.
Contributor: Jan-H. Jagla, January 2010
$offText
*Solution of problem 9.2.2 on the web
scalar x_l / 10 /
y_l / 10 /
tol / 1e-6 /;
variables z, z_in, y; positive variable x;
equations ob, o1, o2, o3, c0, c1, c2, c3;
ob.. sqr(x) + sqr(y-10) =e= z;
o1.. x =l= 15;
o2.. - x + y =l= 0;
o3.. - x =l= 0;
c0.. 2*y*(x + y - 30) =e= z_in;
c1.. x + y =l= 20;
c2.. - y =l= 0;
c3.. y =l= 20;
model bilevel / all /;
$echo bilevel x max z_in y c0 c1 c2 c3 > "%emp.info%"
*Start from reported solution
x.l = x_l;
y.l = y_l;
solve bilevel using EMP minimizing z;
abort$( (abs(x.l - x_l) > tol)
or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';