$title Practical Bilevel Optimization Example 8.7.1 (BARD871,SEQ=8) $ontext 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 $offtext *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';