$title Bilevel model with and without explicitly defined objective equation (EMPBP04,SEQ=465)

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The KKT conditions generated for a inner problem with a well-defined
objective equation (defobj) need to be the same as if the objective is not
defined explicitly.

Contributor: Jan-H. Jagla, November 2009

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variables x, y, obj;

equations upper, lower, defobj;
upper.. y =g= x;
lower.. y =g= -x;
defobj.. obj =e= y;
model implicit /upper,lower/;
model explicit /all/;

x.lo = -2;
x.l = x.lo;
y.l = 2;
lower.m = EPS;

execute 'echo FileName explicit.gms > jams.opt';
execute 'echo bilevel min obj y defobj lower > "%emp.info%"';
explicit.optfile = 1;
solve explicit using emp min x;

execute 'echo FileName implicit.gms > jams.op2';
execute 'echo bilevel min y lower > "%emp.info%"';
implicit.optfile = 2;
solve implicit using emp min x;

execute 'diff -bw explicit.gms implicit.gms'
abort$errorlevel 'explicit.gms and implicit.gms differ';