Generalization of an existence theorem for variational inequalities

CSpace

	Generalization of an existence theorem for variational inequalities
	Huang, ZH
	2003-09-01
发表期刊	JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN	0022-3239
卷号	118 期号:3 页码:567-585
摘要	By using the concept of exceptional family of elements, Zhao proposed a new existence theorem for variational inequalities over a general nonempty closed convex set (Ref. 1, Theorem 2.3), which is a generalization of the well-known More's existence theorem for nonlinear complementarity problems. The proof of Theorem 2.3 in Ref. 1 depends strongly on the condition 0epsilonK. Since this condition is rather strict for a general variational inequality, Zhao proposed an open question at the end of Ref. 1: Can the condition 0epsilonK in Theorem 2.3 be removed? In this paper, we answer this open question. Furthermore, we present the new notion of exceptional family of elements and establish a theorem of the alternative, by which we develop two new existence theorems for variational inequalities. Our results generalize the Zhao existence result.
关键词	variational inequalities complementarity problems exceptional family of elements existence theorem
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000186732200005
出版者	KLUWER ACADEMIC/PLENUM PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19017
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, ZH
作者单位	Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Huang, ZH. Generalization of an existence theorem for variational inequalities[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2003,118(3):567-585.
APA	Huang, ZH.(2003).Generalization of an existence theorem for variational inequalities.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,118(3),567-585.
MLA	Huang, ZH."Generalization of an existence theorem for variational inequalities".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 118.3(2003):567-585.