Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities

被引：26

作者：

He, Songnian ^{[1
]}

Xu, Hong-Kun ^{[2
]}

机构：

[1] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2013年 / 57卷 / 04期

关键词：

Supporting hyperplane; Uniqueness; Variational inequality; Alternative; Hilbert space; DESCENT METHODS;

D O I：

10.1007/s10898-012-9995-z

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：

A uniqueness theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Three examples are given to demonstrate the usefulness and advantages of our alternative theorem.

引用

页码：1375 / 1384

页数：10

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