flds914.gms : Princeton Bilevel Optimization Example 9.1.4

Description

```Test problem 9.2.5 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.4 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.

Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
```

Small Model of Type : BP

Category : GAMS EMP library

Main file : flds914.gms

``````\$title Princeton Bilevel Optimization Example 9.1.4 (FLDS914,SEQ=30)

\$ontext

Test problem 9.2.5 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.4 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.

Contributor: Alex Meeraus and Jan-H. Jagla, December 2009

\$offtext

*Solution of problem 9.1.2 on the web
scalar x_l /   19 /
y_l /   14 /
tol / 1e-6 /;

variables z; positive variable x, y;
equations ob, c2, c3, c4;

ob..      x - 4*y =e=   z;

c2..  - 2*x +   y =l=   0;
c3..    2*x + 5*y =l= 108;
c4..    2*x - 3*y =l=  -4;

model bilevel / all /;

\$echo bilevel x min y c2 c3 c4 > "%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';
``````
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