Abstract and Applied Analysis
Volume 2012 (2012), Article ID 935673, 9 pages
http://dx.doi.org/10.1155/2012/935673
Research Article

Weak Sharp Minima in Set-Valued Optimization Problems

Ming-hao Jin,1 Jun-xiang Wang,2 and Shu Xu3

1Department of Mathematics, Heilongjiang Institute of Technology, Harbin 150050, China
2Office of Academic Affairs, Heilongjiang Institute of Technology, Haerbin 150050, China
3Rear Services Office, Chongqing Police College, Chongqing 401331, China

Received 12 October 2012; Accepted 27 November 2012

Academic Editor: Guanglu Zhou

Copyright © 2012 Ming-hao Jin et al. 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 introduce the notion of a weak ψ-sharp minimizer for set-valued optimization problems. We present some sufficient and necessary conditions that a pair point is a weak ψ-sharp minimizer through the outer limit of set-valued map and develop the characterization of the weak ψ-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones in Studniarski (2007).