$title Princeton Bilevel Optimization Example 9.2.5 (FLDS925,SEQ=40)

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  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

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*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';