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向量均衡问题的超有效性的对偶形式
引用本文: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
作者姓名:龚舒  龚循华
作者单位:1. 南昌大学数学系,南昌 330031
基金项目:国家自然科学基金 (Nos. 11061023, 11201216)
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  
收稿时间:2012-03-01

Dual forms of super efficiency for vector equilibrium problems
GONG Shu , GONG Xunhua. Dual forms of super efficiency for vector equilibrium problems[J]. OR Transactions, 2013, 17(2): 107-123
Authors:GONG Shu    GONG Xunhua
Affiliation:1. Department of Mathematics, Nanchang University, Nanchang 330031, China
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.
Keywords:vector equilibrium problems  vector optimization  strongly superefficient solution  weakly superefficient solution  homogeneously superefficient solution  dual form
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