Description
Test problem 9.3.6 in Handbook of Test Problems in Local and Global Optimization Test problem 9.2.5 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 Clark, P A, and Westerberg, A W, Bilevel Programming for Steady-State Chemical Process Design-i. Fundamentals and Algorithms. Comput. Chem. Eng. 14 (1990), 87-97. Contributor: Jan-H. Jagla, January 2010
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds925.gms
$title Princeton Bilevel Optimization Example 9.2.5 (FLDS925,SEQ=40)
$onText
Test problem 9.3.6 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.2.5 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
Clark, P A, and Westerberg, A W, Bilevel Programming for Steady-State Chemical
Process Design-i. Fundamentals and Algorithms. Comput. Chem. Eng. 14 (1990), 87-97.
Contributor: Jan-H. Jagla, January 2010
$offText
*Solution of problem 9.2.5 on the web
scalar x_l / 1 /
y_l / 3 /
tol / 1e-6 /;
variables z, z_in, y; positive variable x;
equations ob, c0, c1, c2, c3;
ob.. sqr(x-3) + sqr(y-2) =e= z;
c0.. sqr(y-5) =e= z_in;
c1.. -2*x + y =l= 1;
c2.. x - 2*y =l= 2;
c3.. x + 2*y =l= 14;
model bilevel / all /;
$echo bilevel x min z_in y c0 c1 c2 c3 > "%emp.info%"
*Start from reported solution
x.l = x_l;
y.l = y_l;
solve bilevel using EMP minimizing z;
abort$( (abs(x.l - x_l) > tol)
or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';