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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 570918, 9 pages
http://dx.doi.org/10.1155/2013/570918
Research Article

Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

1Department of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Chongqing Police College, Chongqing 401331, China
3Basic Course Department, Nanchang Institute of Science and Technology, Nanchang 330108, China

Received 10 December 2012; Revised 6 March 2013; Accepted 11 March 2013

Academic Editor: Sheng-Jie Li

Copyright © 2013 Xiaohong Hu 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

The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.