Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 183297, 15 pages
doi:10.1155/2011/183297
Research Article

Optimality Conditions of Vector Set-Valued Optimization Problem Involving Relative Interior

Zhiang Zhou1,2

1College of Sciences, Shanghai University, Shanghai 200444, China
2Department of Applied Mathematics, Chongqing University of Technology, Chongqing 400054, China

Received 26 October 2010; Revised 25 December 2010; Accepted 22 January 2011

Academic Editor: Sin E. Takahasi

Copyright © 2011 Zhiang Zhou. 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

Firstly, a generalized weak convexlike set-valued map involving the relative interior is introduced in separated locally convex spaces. Secondly, a separation property is established. Finally, some optimality conditions, including the generalized Kuhn-Tucker condition and scalarization theorem, are obtained.