$title Practical Bilevel Optimization Example 5.1.1 (BARD511,SEQ=4)

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Example from Chapter 5, example 5.1.1, page 197

John F. Bard, Practical Bilevel Optimization: Algorithms and Applications,
Kluwer Academic Publishers, Dordrecht, 1998.

Contributor: Jan-H. Jagla, January 2009

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positive variables x,y; variables objout,objin;
equations defout,defin,e1,e2,e3,e4;

defout.. objout =e= x - 4*y;
defin..  objin  =e= y;

e1..    - x -   y =l= -3;
e2..   -2*x +   y =l=  0;
e3..    2*x +   y =l= 12;
e4..    3*x - 2*y =l=  4;

model bard / all /;

$echo bilevel x min objin y defin e1 e2 e3 e4 > "%emp.info%"

solve bard us emp min objout;

*Note: The subsolver used by EMP might not find the global solution
parameter solution(*,*);
solution('x','book') = 4;  solution('x','model') = x.l;
solution('y','book') = 4;  solution('y','model') = y.l;
display solution;