Description
Test problem 9.3.7 in Handbook of Test Problems in Local and Global Optimization Test problem 9.2.6 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 Falk, J. E. and Liu, J. (1995). On bilevel programming, Part I: General nonlinear cases. Mathematical Programming, 70:47-72. Contributor: Jan-H. Jagla, January 2010
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds926.gms
$title Princeton Bilevel Optimization Example 9.2.6 (FLDS926,SEQ=41)
$onText
Test problem 9.3.7 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.2.6 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
Falk, J. E. and Liu, J. (1995). On bilevel programming, Part I: General
nonlinear cases. Mathematical Programming, 70:47-72.
Contributor: Jan-H. Jagla, January 2010
$offText
*Solution of problem 9.2.6 on the web
scalar x1_l / 0.5 /
x2_l / 0.5 /
y1_l / 0.5 /
y2_l / 0.5 /
tol / 1e-6 /;
variables z, z_in, y1, y2; positive variable x1, x2;
equations ob, c0, c1, c2, c3, c4;
ob.. sqr(x1) - 2*x1 + sqr(x2) - 2*x2 + sqr(y1) + sqr(y2) =e= z;
c0.. sqr(y1-x1) + sqr(y2-x2) =e= z_in;
c1.. - y1 =l= -0.5;
c2.. - y2 =l= -0.5;
c3.. y1 =l= 1.5;
c4.. y2 =l= 1.5;
model bilevel / all /;
$echo bilevel x1 x2 min z_in y1 y2 c0 c1 c2 c3 c4 > "%emp.info%"
*Start from reported solution
x1.l = x1_l;
x2.l = x2_l;
y1.l = y1_l;
y2.l = y2_l;
solve bilevel using EMP minimizing z;
abort$( (abs(x1.l - x1_l) > tol)
or (abs(x2.l - x2_l) > tol)
or (abs(y1.l - y1_l) > tol)
or (abs(y2.l - y2_l) > tol) ) 'Deviated from reported solution';