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Abstract and Applied Analysis
Volume 2014, Article ID 948270, 8 pages
http://dx.doi.org/10.1155/2014/948270
Research Article

Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps

School of Mathematics and Statistics, Xidian University, Xi’an 710071, China

Received 22 June 2014; Accepted 10 August 2014; Published 27 August 2014

Academic Editor: S. D. Purohit

Copyright © 2014 Yanfei Chai 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

We first obtain that subdifferentials of set-valued mapping from finite-dimensional spaces to finite-dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational-like inequalities which are defined by means of subdifferentials. Finally, an existence result of generalized weakly efficient solutions for vector optimization problem involving a subdifferentiable and preinvex set-valued mapping is established by exploiting the existence of a solution for the weak formulation of the generalized Stampacchia vector variational-like inequality via a Fan-KKM lemma.