Differential properties and optimality conditions for generalized weak vector variational inequalities
In this paper, we study a generalized weak vector variational inequality, which is a generalization of a weak vector variational inequality and a Minty weak vector variational inequality. By virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
2013
|
| Online Access: | http://hdl.handle.net/20.500.11937/45897 |
| _version_ | 1848757411755589632 |
|---|---|
| author | Zhu, S. Li, S. Teo, Kok Lay |
| author_facet | Zhu, S. Li, S. Teo, Kok Lay |
| author_sort | Zhu, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we study a generalized weak vector variational inequality, which is a generalization of a weak vector variational inequality and a Minty weak vector variational inequality. By virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class of set-valued maps and obtain an explicit expression of its contingent derivative. We also establish some necessary optimality conditions for solutions of the generalized weak vector variational inequality, which generalize the corresponding results in the literature. Furthermore, we establish some unified necessary and sufficient optimality conditions for local optimal solutions of the generalized weak vector variational inequality. Simultaneously, we also show that there is no gap between the necessary and sufficient conditions under an appropriate condition. |
| first_indexed | 2025-11-14T09:27:40Z |
| format | Journal Article |
| id | curtin-20.500.11937-45897 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:27:40Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-458972017-09-13T14:24:47Z Differential properties and optimality conditions for generalized weak vector variational inequalities Zhu, S. Li, S. Teo, Kok Lay In this paper, we study a generalized weak vector variational inequality, which is a generalization of a weak vector variational inequality and a Minty weak vector variational inequality. By virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class of set-valued maps and obtain an explicit expression of its contingent derivative. We also establish some necessary optimality conditions for solutions of the generalized weak vector variational inequality, which generalize the corresponding results in the literature. Furthermore, we establish some unified necessary and sufficient optimality conditions for local optimal solutions of the generalized weak vector variational inequality. Simultaneously, we also show that there is no gap between the necessary and sufficient conditions under an appropriate condition. 2013 Journal Article http://hdl.handle.net/20.500.11937/45897 10.1007/s11117-012-0179-3 restricted |
| spellingShingle | Zhu, S. Li, S. Teo, Kok Lay Differential properties and optimality conditions for generalized weak vector variational inequalities |
| title | Differential properties and optimality conditions for generalized weak vector variational inequalities |
| title_full | Differential properties and optimality conditions for generalized weak vector variational inequalities |
| title_fullStr | Differential properties and optimality conditions for generalized weak vector variational inequalities |
| title_full_unstemmed | Differential properties and optimality conditions for generalized weak vector variational inequalities |
| title_short | Differential properties and optimality conditions for generalized weak vector variational inequalities |
| title_sort | differential properties and optimality conditions for generalized weak vector variational inequalities |
| url | http://hdl.handle.net/20.500.11937/45897 |