Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces
The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the norma...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/128178 |
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| _version_ | 1832562805162639360 |
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| author | Si-Huan Li Qiang Wang Shu Xu Jun-Xiang Wang |
| author_facet | Si-Huan Li Qiang Wang Shu Xu Jun-Xiang Wang |
| author_sort | Si-Huan Li |
| collection | DOAJ |
| description | The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively. |
| format | Article |
| id | doaj-art-51961e7d23394c2aad08ae02f5f1aa04 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51961e7d23394c2aad08ae02f5f1aa042025-02-03T01:21:38ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/128178128178Sharp Efficiency for Vector Equilibrium Problems on Banach SpacesSi-Huan Li0Qiang Wang1Shu Xu2Jun-Xiang Wang3School of Economics and Business Administration, Chongqing University, Chongqing 400030, ChinaAutomobile and Traffic Engineering College, Heilongjiang Institute of Technology, Harbin 150050, ChinaRear Services Office, Chongqing Police College, Chongqing 401331, ChinaOffice of Academic Affairs, Heilongjiang Institute of Technology, Harbin 150050, ChinaThe concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.http://dx.doi.org/10.1155/2013/128178 |
| spellingShingle | Si-Huan Li Qiang Wang Shu Xu Jun-Xiang Wang Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces Abstract and Applied Analysis |
| title | Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces |
| title_full | Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces |
| title_fullStr | Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces |
| title_full_unstemmed | Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces |
| title_short | Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces |
| title_sort | sharp efficiency for vector equilibrium problems on banach spaces |
| url | http://dx.doi.org/10.1155/2013/128178 |
| work_keys_str_mv | AT sihuanli sharpefficiencyforvectorequilibriumproblemsonbanachspaces AT qiangwang sharpefficiencyforvectorequilibriumproblemsonbanachspaces AT shuxu sharpefficiencyforvectorequilibriumproblemsonbanachspaces AT junxiangwang sharpefficiencyforvectorequilibriumproblemsonbanachspaces |