向量优化问题的ε-有效性(英文)  

ε-Efficiency in Vector Optimization Problems

作　　者：赵克全[1] 万轩[1] 彭婕[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2012年第5期6-9,共4页Journal of Chongqing Normal University:Natural Science

基　　金：The National Science Foundation of China(No.11126348;No.11171363);the Natural Science Foundation Project of Chongqing(No.2011BA0030);the Special Fund of Chongqing Key Laboratory(No.CSTC2011KLORSE02);the Education Committee Research Foundation of Chongqing(No.KJ110625)

摘　　要：研究了一类向量优化问题的ε-有效性和两类真有效性,包括ε-Benson真有效性和ε-Geoffrion真有效性。首先证明了这两类真有效性之间的等价关系。同时,利用Benson标量化方法给出了向量优化问题的ε-有效解的一些标量化结果。x0是问题(VP)的ε-有效解当且仅当对应于问题(VP)的表量化问题(VPv)有Ψ=0。本文的主要结果不仅是对一些已有结果的改进与推广,而且也表明戎卫东与马毅提出的ε-真有效性与Liu Jen-chwan提出的ε-真有效性的一致性。In this paper, a class of vector optimization problems is considered and e-efficiency and two kinds ot proper efficiency, namely ε-Benson proper efficiency and ε-Geoffrion proper efficiency are investigated. The equivalence is proved for two kinds of e -proper efficiency, At the same time, e-efficiency is characterized by making use of the clas sic scalarization method named as Benson＇s method which was introduced by Benson：x0 is an s-efficient solution of problem （VP） if and only if ψ=0 for the scalar optimization problem （VPv） corresponds to （VP）. Our results not only improve and generalize some known results and hut also show that e-proper efficiency introduced by Rong Wei- dong and Ma Yi coincides with e-proper efficiency introduced by Liu Jen-chwan.

关 键 词：向量优化 ε-有效性 ε-真有效性 标量化 

分 类 号：O221.6[理学—运筹学与控制论]