Abstract and Applied Analysis
Volume 2013 (2013), Article ID 128178, 6 pages
http://dx.doi.org/10.1155/2013/128178
Research Article

Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces

Si-Huan Li,1,2 Qiang Wang,3 Shu Xu,4 and Jun-Xiang Wang5

1School of Economics and Business Administration, Chongqing University, Chongqing 400030, China
2Department of Business Administration, Huaihua University, Huaihua, Hunan 418000, China
3Automobile and Traffic Engineering College, Heilongjiang Institute of Technology, Harbin 150050, China
4Rear Services Office, Chongqing Police College, Chongqing 401331, China
5Office of Academic Affairs, Heilongjiang Institute of Technology, Harbin 150050, China

Received 31 December 2012; Accepted 27 February 2013

Academic Editor: Qun Lin

Copyright © 2013 Si-Huan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.