Nonemptiness and boundedness of solution sets for vector variational inequalities via topological method

被引：2

作者：

Fan, Jiang-hua ^{[1
]}

Jing, Yan ^{[1
]}

Zhong, Ren-you ^{[1
]}

机构：

[1] Guangxi Normal Univ, Dept Math, Guilin 541004, Guangxi, Peoples R China

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2015年 / 63卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Vector variational inequality; Nonemptiness and boundedness; C-pseudomonotone; Connectedness; Recession cone; CONVEX; COMPACTNESS; EXISTENCE;

D O I：

10.1007/s10898-015-0279-2

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：

In this paper, some characterizations of nonemptiness and boundedness of solution sets for vector variational inequalities are studied in finite and infinite dimensional spaces, respectively. By using a new proof method which is different from the one used in Huang et al. (J Optim Theory Appl 162:548-558 2014), a sufficient and necessary condition for the nonemptiness and boundedness of solution sets is established. Basing on this result, some new characterizations of nonemptiness and boundedness of solution sets for vector variational inequalities are proved. Compared with the known results in Huang et al. (2014), the key assumption that is not required in finite dimensional spaces. Furthermore, the corresponding result of Huang et al. (2014) is extended to the case of infinite dimensional spaces. Some examples are also given to illustrated the main results.

引用

页码：181 / 193

页数：13