Description
Example from Chapter 8, example 8.7.1, page 358 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 : bard871.gms
$title Practical Bilevel Optimization Example 8.7.1 (BARD871,SEQ=8)
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Example from Chapter 8, example 8.7.1, page 358
John F. Bard, Practical Bilevel Optimization: Algorithms and Applications,
Kluwer Academic Publishers, Dordrecht, 1998.
Contributor: Jan-H. Jagla, January 2009
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*The reported solution is
scalar x_l /11.25/
y_l / 5/
tol / 1e-3/;
positive variables x,y; variables objout,objin;
equations defout,defin,e1,e2;
defout.. objout =e= 16*sqr(x) + 9*sqr(y);
defin.. objin =e= power(x+y-20,4);
e1.. -4*x + y =l= 0;
e2.. 4*x + y =l= 50;
model bard / all /;
$echo bilevel x min objin y defin e2 > "%emp.info%"
*Start from reported solution
x.l = x_l ;
y.l = y_l;
solve bard us emp min objout;
abort$( (abs(x.l - x_l ) > tol)
or (abs(y.l - y_l ) > tol) ) 'Deviated from known solution';