Open Access

Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems

Journal of Inequalities and Applications20082008:678014

DOI: 10.1155/2008/678014

Received: 9 January 2008

Accepted: 4 April 2008

Published: 14 April 2008

Abstract

We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmooth vector optimization problems by using the equivalence and Fan-KKM theorem under some suitable conditions.

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Authors’ Affiliations

(1)
Department of Applied Mathematics, Southwest Petroleum University
(2)
Department of Mathematics, Kyungnam University
(3)
Department of Mathematics, Sichuan University

Copyright

© Zhi-Bin Liu et al. 2008

This article is published under license to BioMed Central Ltd. 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.