Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 370654, 9 pages
http://dx.doi.org/10.1155/2012/370654
Research Article

A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces

1College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
2School of Mathematics, Chongqing Normal University, Chongqing 400047, China

Received 24 June 2012; Accepted 26 July 2012

Academic Editor: Nan-Jing Huang

Copyright © 2012 Zhi-Ang Zhou and Jian-Wen Peng. 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

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimization problems were established in the sense of globally proper efficiency.