Bilevel programs with extremal value function: global optimality release_qhhwthp66bcxnmy4eznkaizdsy

by Abdelmalek Aboussoror, Hicham Babahadda, Abdelatif Mansouri

Published in International Journal of Mathematics and Mathematical Sciences by Hindawi Limited.

2005   Volume 2005, p419-435

Abstract

For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$Max$" id="E1"><mml:mtext>max</mml:mtext></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$Min$" id="E2"><mml:mtext>min</mml:mtext></mml:math>problem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.
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