On Gap Functions for Quasi-Variational Inequalities
For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalitie...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/531361 |
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| _version_ | 1850106045509140480 |
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| author | Kouichi Taji |
| author_facet | Kouichi Taji |
| author_sort | Kouichi Taji |
| collection | DOAJ |
| description | For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable. |
| format | Article |
| id | doaj-art-30f9ec1ca9bf466183fb8292d381a9e1 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-30f9ec1ca9bf466183fb8292d381a9e12025-08-20T02:38:54ZengWileyAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/531361531361On Gap Functions for Quasi-Variational InequalitiesKouichi Taji0Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, JapanFor variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable.http://dx.doi.org/10.1155/2008/531361 |
| spellingShingle | Kouichi Taji On Gap Functions for Quasi-Variational Inequalities Abstract and Applied Analysis |
| title | On Gap Functions for Quasi-Variational Inequalities |
| title_full | On Gap Functions for Quasi-Variational Inequalities |
| title_fullStr | On Gap Functions for Quasi-Variational Inequalities |
| title_full_unstemmed | On Gap Functions for Quasi-Variational Inequalities |
| title_short | On Gap Functions for Quasi-Variational Inequalities |
| title_sort | on gap functions for quasi variational inequalities |
| url | http://dx.doi.org/10.1155/2008/531361 |
| work_keys_str_mv | AT kouichitaji ongapfunctionsforquasivariationalinequalities |