Description
Example from Chapter 7, example 7.2.1, page 275 John F. Bard, Practical Bilevel Optimization: Algorithms and Applications, Kluwer Academic Publishers, Dordrecht, 1998. Contributor: Jan-H. Jagla, January 2009
Small Model of Type : BP
Category : GAMS EMP library
Main file : bard721.gms
$title Practical Bilevel Optimization Example 7.2.1 (BARD721,SEQ=5)
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Example from Chapter 7, example 7.2.1, page 275
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 x1,x2,y; variables objout,objin;
equations defout,defin;
defout.. objout =e= 1/2*sqr(x1-4/5) + 1/2*sqr(x2-1/5) + 1/2*sqr(y-1);
defin.. objin =e= 1/2*sqr(y) - y - x1*y + 2*x2*y;
x1.up = 1; x2.up=1; y.up = 1;
model bard / all /;
$echo bilevel x1 x2 min objin y defin > "%emp.info%"
solve bard us emp min objout;
*Note: The subsolver used by EMP might not find the global solution
parameter solution(*,*);
solution('x1','book') = 0.8; solution('x1','model') = x1.l;
solution('x2','book') = 0.2; solution('x2','model') = x2.l;
solution('y' ,'book') = 1 ; solution('y' ,'model') = y.l;
display solution;