<p>Optimality Conditions of Vector Set-Valued Optimization Problem Involving Relative Interior</p>

1029-242X-2011-183297 1029-242X Research Article <p>Optimality Conditions of Vector Set-Valued Optimization Problem Involving Relative Interior</p> ZhouZhiangzhi_ang@163.com

College of Sciences, Shanghai University, Shanghai 200444, China

Department of Applied Mathematics, Chongqing University of Technology, Chongqing 400054, China

Journal of Inequalities and Applications 1029-242X 2011 2011 1 183297 http://www.journalofinequalitiesandapplications.com/content/2011/1/183297 10.1155/2011/183297 26102010251220102212011822011 2011Zhiang 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.

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