$title Princeton Bilevel Optimization Example 9.2.6 (FLDS926,SEQ=41)

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  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

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*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';