On Penalty and Gap Function Methods for Bilevel Equilibrium Problems
We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇-monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap functio...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/646452 |
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| _version_ | 1850229640099004416 |
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| author | Bui Van Dinh Le Dung Muu |
| author_facet | Bui Van Dinh Le Dung Muu |
| author_sort | Bui Van Dinh |
| collection | DOAJ |
| description | We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇-monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case that arises from the Tikhonov regularization method for pseudomonotone equilibrium problems. |
| format | Article |
| id | doaj-art-2aa575cf4b924cbd89bb55164ba3724a |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2aa575cf4b924cbd89bb55164ba3724a2025-08-20T02:04:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/646452646452On Penalty and Gap Function Methods for Bilevel Equilibrium ProblemsBui Van Dinh0Le Dung Muu1Faculty of Information Technology, Le Quy Don University, Hanoi, VietnamControl and Optimization Department, Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi 10307, VietnamWe consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇-monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case that arises from the Tikhonov regularization method for pseudomonotone equilibrium problems.http://dx.doi.org/10.1155/2011/646452 |
| spellingShingle | Bui Van Dinh Le Dung Muu On Penalty and Gap Function Methods for Bilevel Equilibrium Problems Journal of Applied Mathematics |
| title | On Penalty and Gap Function Methods for Bilevel Equilibrium Problems |
| title_full | On Penalty and Gap Function Methods for Bilevel Equilibrium Problems |
| title_fullStr | On Penalty and Gap Function Methods for Bilevel Equilibrium Problems |
| title_full_unstemmed | On Penalty and Gap Function Methods for Bilevel Equilibrium Problems |
| title_short | On Penalty and Gap Function Methods for Bilevel Equilibrium Problems |
| title_sort | on penalty and gap function methods for bilevel equilibrium problems |
| url | http://dx.doi.org/10.1155/2011/646452 |
| work_keys_str_mv | AT buivandinh onpenaltyandgapfunctionmethodsforbilevelequilibriumproblems AT ledungmuu onpenaltyandgapfunctionmethodsforbilevelequilibriumproblems |