Gap function for set-valued vector variational-like inequalities

被引：3

作者：

Mishra, S. K. ^{[1
,2
]}

Wang, S. Y. ^{[3
]}

Lai, K. K. ^{[2
]}

机构：

[1] Govind Ballabh Pant Univ Agr & Technol, Dept Math & Stat, Coll Basic Sci & Humanities, Pantnagar 263145, Uttar Pradesh, India

[2] City Univ Hong Kong, Dept Management Sci, Kowloon, Hong Kong, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2008年 / 138卷 / 01期

关键词：

vector variational-like inequalities; set-valued mappings; gap functions; existence of a solution; semidefinite programming;

D O I：

10.1007/s10957-008-9401-7

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：

Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities (VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem.

引用

页码：77 / 84

页数：8

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