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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.419 |
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| _version_ | 1832562725248565248 |
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| author | Abdelmalek Aboussoror Hicham Babahadda Abdelatif Mansouri |
| author_facet | Abdelmalek Aboussoror Hicham Babahadda Abdelatif Mansouri |
| author_sort | Abdelmalek Aboussoror |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-3b1781c5486549e3ac070f3c18e7600d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3b1781c5486549e3ac070f3c18e7600d2025-02-03T01:21:48ZengWileyInternational 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 |
| spellingShingle | Abdelmalek Aboussoror Hicham Babahadda Abdelatif Mansouri Bilevel programs with extremal value function: global optimality International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Bilevel programs with extremal value function: global optimality |
| title_sort | bilevel programs with extremal value function global optimality |
| url | http://dx.doi.org/10.1155/IJMMS.2005.419 |
| work_keys_str_mv | AT abdelmalekaboussoror bilevelprogramswithextremalvaluefunctionglobaloptimality AT hichambabahadda bilevelprogramswithextremalvaluefunctionglobaloptimality AT abdelatifmansouri bilevelprogramswithextremalvaluefunctionglobaloptimality |