Bilevel programs with extremal value function: global optimality

Bilevel programs with extremal value function: global optimality

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 give...

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Main Authors: Abdelmalek Aboussoror, Hicham Babahadda, Abdelatif Mansouri
Format: Article
Language:English
Published: Hindawi Limited 2005-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS.2005.419
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spelling doaj-3b1781c5486549e3ac070f3c18e7600d2020-11-25T00:43:25ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005341943510.1155/IJMMS.2005.419Bilevel programs with extremal value function: global optimalityAbdelmalek Aboussoror0Hicham Babahadda1Abdelatif Mansouri2Centre des Études Universitaires de Safi, Université Cadi Ayyad, Sidi Bouzid, P.O. Box 4162, Safi, MoroccoDépartement de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, P.O. Box 2390, Marrakech 40000, MoroccoDépartement de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, P.O. Box 2390, Marrakech 40000, MoroccoFor 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.http://dx.doi.org/10.1155/IJMMS.2005.419
collection DOAJ
language English
format Article
sources DOAJ
author Abdelmalek Aboussoror
Hicham Babahadda
Abdelatif Mansouri
spellingShingle Abdelmalek Aboussoror
Hicham Babahadda
Abdelatif Mansouri
Bilevel programs with extremal value function: global optimality
International Journal of Mathematics and Mathematical Sciences
author_facet Abdelmalek Aboussoror
Hicham Babahadda
Abdelatif Mansouri
author_sort Abdelmalek Aboussoror
title Bilevel programs with extremal value function: global optimality
title_short Bilevel programs with extremal value function: global optimality
title_full Bilevel programs with extremal value function: global optimality
title_fullStr Bilevel programs with extremal value function: global optimality
title_full_unstemmed Bilevel programs with extremal value function: global optimality
title_sort bilevel programs with extremal value function: global optimality
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2005-01-01
description 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.
url http://dx.doi.org/10.1155/IJMMS.2005.419
work_keys_str_mv AT abdelmalekaboussoror bilevelprogramswithextremalvaluefunctionglobaloptimality
AT hichambabahadda bilevelprogramswithextremalvaluefunctionglobaloptimality
AT abdelatifmansouri bilevelprogramswithextremalvaluefunctionglobaloptimality
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