Open Access

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

Journal of Inequalities and Applications20112011:183297

https://doi.org/10.1155/2011/183297

Received: 26 October 2010

Accepted: 22 January 2011

Published: 8 February 2011

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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Authors’ Affiliations

(1)
College of Sciences, Shanghai University, Shanghai, China
(2)
Department of Applied Mathematics, Chongqing University of Technology, Chongqing, China

Copyright

© 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.