Description

Test problem 9.2.7 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.6 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.

G. Anandalingam and D. J. White, "A Solution Method for the Linear Static
Stackelberg Problem Using Penalty Functions", IEEE Transactions on Automatic
Control, vol. 35, no. 10, pp 1170-1173, 1990.

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

Small Model of Type : BP

Category : GAMS EMP library

Main file : flds916.gms

$title Princeton Bilevel Optimization Example 9.1.6 (FLDS916,SEQ=32)

$onText

  Test problem 9.2.7 in Handbook of Test Problems in Local and Global Optimization
  Test problem 9.1.6 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.

G. Anandalingam and D. J. White, "A Solution Method for the Linear Static
Stackelberg Problem Using Penalty Functions", IEEE Transactions on Automatic
Control, vol. 35, no. 10, pp 1170-1173, 1990.

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

$offText

*Solution of problem 9.1.6 on the web
scalar  x_l /   16 /
        y_l /   11 /
        tol / 1e-6 /;

variables z, z_in; positive variable x, y;
equations ob, ob_in, c1, c2, c3, c4, c5, c6;

ob..      -   x - 3*y =e= z;

ob_in..         - 3*y =e= z_in;
c1..      -   x - 2*y =l= -10;
c2..          x - 2*y =l=   6;
c3..        2*x -   y =l=  21;
c4..          x + 2*y =l=  38;
c5..      -   x + 2*y =l=  18;
c6..            -   y =l=   0;


model bilevel / all /;

$echo bilevel x max z_in y ob_in c1 c2 c3 c4 c5 c6 > "%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';