Journal of Applied Mathematics
Volume 2011 (2011), Article ID 647489, 16 pages
http://dx.doi.org/10.1155/2011/647489
Research Article

Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

Xin-kun Wu,1 Jia-wei Chen,2 and Yun-zhi Zou1

1College of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China

Received 13 May 2011; Accepted 10 July 2011

Academic Editor: Yongkun Li

Copyright © 2011 Xin-kun Wu 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

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.