向量均衡问题的超有效性的对偶形式

运筹学学报 ›› 2013, Vol. 17 ›› Issue (2): 107-123.

向量均衡问题的超有效性的对偶形式

龚舒¹，龚循华^1,*

1. 南昌大学数学系，南昌 330031

收稿日期:2012-03-01 出版日期:2013-06-15 发布日期:2013-06-15
通讯作者: 龚循华 E-mail:xunhuagong@gmail.com
基金资助:
国家自然科学基金 (Nos. 11061023, 11201216)

Dual forms of super efficiency for vector equilibrium problems

GONG Shu¹,GONG Xunhua^1,*

1. Department of Mathematics, Nanchang University, Nanchang 330031, China

Received:2012-03-01 Online:2013-06-15 Published:2013-06-15

摘要/Abstract

摘要： 在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念，并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解， C-超有效解， C-齐次超有效解，以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性，并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用，给出了向量优化问题各种超有效解的对偶形式.

关键词: 向量均衡问题, 向量优化, 强超有效解, 弱超有效解, 齐次超有效解, 对偶形式

Abstract: The paper introduces the concepts of strongly superefficient solution, C-strongly superefficient solution, weakly superefficient solution, C-weakly superefficient solution, homogeneously superefficient solution and C-homogeneously superefficient solution for vector equilibrium problems, and discusses the dual forms of C-weakly superefficient solution, C-superefficient solution, C-homogeneously superefficient solution, C-strongly superefficient solution, respectively for vector equilibrium problems in locally convex space with the aid of polar theory. The equivalence of the above kinds of superefficiencies in the normed space was studied, and their dual forms for vector equilibrium problems in the normed space with a normal cone were discussed. As an application, the dual forms of various superefficiencies are given for vector optimization problems.

Key words: vector equilibrium problems, vector optimization, strongly superefficient solution, weakly superefficient solution, homogeneously superefficient solution, dual form

中图分类号:

O223
O178

龚舒，龚循华. 向量均衡问题的超有效性的对偶形式[J]. 运筹学学报, 2013, 17(2): 107-123.

GONG Shu,GONG Xunhua. Dual forms of super efficiency for vector equilibrium problems[J]. Operations Research Transactions, 2013, 17(2): 107-123.

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