Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces

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: Si-Huan Li, Qiang Wang, Shu Xu, Jun-Xiang Wang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/128178
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spelling doaj-51961e7d23394c2aad08ae02f5f1aa042020-11-24T22:31:32ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Si-Huan Li
Qiang Wang
Shu Xu
Jun-Xiang Wang
spellingShingle Si-Huan Li
Qiang Wang
Shu Xu
Jun-Xiang Wang
Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces
Abstract and Applied Analysis
author_facet Si-Huan Li
Qiang Wang
Shu Xu
Jun-Xiang Wang
author_sort Si-Huan Li
title Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces
title_short 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_sort sharp efficiency for vector equilibrium problems on banach spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
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.
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
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