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向量优化问题的ε-有效性（英文）
  • ISSN号：1672-6693
  • 期刊名称：《重庆师范大学学报：自然科学版》
  • 时间：0
  • 分类：O221.6[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]重庆师范大学数学学院,重庆400047
  • 相关基金：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)
作者： 赵克全[1], 万轩[1], 彭婕[1]
关键词： 向量优化, ε-有效性, ε-真有效性, 标量化, vector optimization, ε-efficiency, e-proper efficiency scalarization
中文摘要：

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。

英文摘要：

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.

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期刊信息
  • 《重庆师范大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:重庆市教育委员会
  • 主办单位:重庆师范大学
  • 主编：杨新民
  • 地址：重庆市沙坪坝区
  • 邮编：400047
  • 邮箱：cqnuj@cqnu.edu.cn
  • 电话：023-65362431
  • 国际标准刊号：ISSN：1672-6693
  • 国内统一刊号：ISSN：50-1165/N
  • 邮发代号:78-34
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  • 被引量:4584