International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 419-435
doi:10.1155/IJMMS.2005.419
Bilevel programs with extremal value function: global optimality
1Centre des Études Universitaires de Safi, Université Cadi Ayyad, Sidi Bouzid, P.O. Box 4162, Safi, Morocco
2Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, P.O. Box 2390, Marrakech 40000, Morocco
Received 4 May 2004; Revised 29 October 2004
Copyright © 2005 Abdelmalek Aboussoror et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 max-min 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.