Abstract and Applied Analysis
Volume 2012 (2012), Article ID 458983, 17 pages
http://dx.doi.org/10.1155/2012/458983
Research Article

On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity

Hehua Jiao1,2 and Sanyang Liu1

1Department of Mathematics, Xidian University, Xi’an 710071, China
2College of Mathematics and Computer, Yangtze Normal University, Fuling 408100, China

Received 4 September 2012; Accepted 12 October 2012

Academic Editor: Ferenc Hartung

Copyright © 2012 Hehua Jiao and Sanyang Liu. 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

By using Clarke’s generalized gradients we consider a nonsmooth vector optimization problem with cone constraints and introduce some generalized cone-invex functions called K-α-generalized invex, K-α-nonsmooth invex, and other related functions. Several sufficient optimality conditions and Mond-Weir type weak and converse duality results are obtained for this problem under the assumptions of the generalized cone invexity. The results presented in this paper generalize and extend the previously known results in this area.