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Open Access

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

Journal of Inequalities and Applications20112011:183297

Received: 26 October 2010

Accepted: 22 January 2011

Published: 8 February 2011


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.


Optimality ConditionFull ArticleConvex SpaceSeparation PropertyRelative Interior

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Authors’ Affiliations

College of Sciences, Shanghai University, Shanghai, China
Department of Applied Mathematics, Chongqing University of Technology, Chongqing, China


© Zhiang Zhou. 2011

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.