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Abstract and Applied Analysis
Volume 2014, Article ID 636907, 5 pages
http://dx.doi.org/10.1155/2014/636907
Research Article

A Kind of Unified Proper Efficiency in Vector Optimization

College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China

Received 22 February 2014; Accepted 14 April 2014; Published 30 April 2014

Academic Editor: Chong Li

Copyright © 2014 Ke Quan Zhao and Yuan Mei Xia. 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

Based on the ideas of the classical Benson proper efficiency, a new kind of unified proper efficiency named S-Benson proper efficiency is introduced by using Assumption (B) proposed by Flores-Bazán and Hernández, which unifies some known exact and approximate proper efficiency including -proper efficiency and E-Benson proper efficiency in vector optimization. Furthermore, a characterization of S-Benson proper efficiency is established via a kind of nonlinear scalarization functions introduced by Göpfert et al.