$title Princeton Bilevel Optimization Example 9.2.2 (FLDS922,SEQ=37)

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  Test problem 9.3.3 in Handbook of Test Problems in Local and Global Optimization
  Test problem 9.2.2 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

Aiyoshi, E and K. Shimizu (1981). Hierarchical Decentralized systems and its
new solution by a Barrier Method. IEEE Trans. Systems, Man and Cybernetics,
SMC-11, 444.

Contributor: Jan-H. Jagla, January 2010

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*Solution of problem 9.2.2 on the web
scalar  x_l /   10 /
        y_l /   10 /
        tol / 1e-6 /;

variables z, z_in, y; positive variable x;
equations ob, o1, o2, o3, c0, c1, c2, c3;

ob..  sqr(x) +       sqr(y-10)  =e=    z;
o1..       x                    =l=   15;
o2..     - x +               y  =l=    0;
o3..     - x                    =l=    0;

c0..           2*y*(x + y - 30) =e= z_in;
c1..       x +               y  =l=   20;
c2..         -               y  =l=    0;
c3..                         y  =l=   20;

model bilevel / all /;

$echo bilevel x max 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';