Gap functions and existence of solutions to set-valued vector variational inequalities

被引：81
|
作者：
Yang, XQ [1 ]
Yao, JC
机构：
[1] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2002年 / 115卷 / 02期
关键词：
vector variational inequalities; set-valued mappings; gap functions; existence of a solution; semi-infinite programming;
D O I：
10.1023/A:1020844423345
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem.
引用
收藏
页码：407 / 417
页数：11
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