Existence results for a class of hemivariational inequality problems on Hadamard manifolds

被引：12

作者：

Tang, Guo-ji ^{[1
,2
]}

Zhou, Li-wen ^{[3
]}

Huang, Nan-jing ^{[4
]}

机构：

[1] Guangxi Univ Nationalities, Guangxi Key Lab Univ Optimizat Control & Engn Cal, Nanning, Peoples R China

[2] Guangxi Univ Nationalities, Sch Sci, Nanning, Peoples R China

[3] Southwest Petr Univ, Sch Sci, Chengdu, Peoples R China

[4] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

来源：

OPTIMIZATION | 2016年 / 65卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Hemivariational inequality; generalized directional derivative; locally Lipschitz function; Fan-KKM lemma; Hadamard manifold; PROXIMAL POINT ALGORITHM; MONOTONE VECTOR-FIELDS; VARIATIONAL-INEQUALITIES; RIEMANNIAN-MANIFOLDS; EQUILIBRIUM PROBLEMS; LIPSCHITZ; SET;

D O I：

10.1080/02331934.2016.1147036

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, a class of hemivariational inequality problems are introduced and studied on Hadamard manifolds. Using the properties of Clarke's generalized directional derivative and Fan-KKM lemma, an existence theorem of solution in connection with the hemivariational inequality problem is obtained when the constraint set is bounded. By employing some coercivity conditions and the properties of Clarke's generalized directional derivative, an existence result and the boundedness of the set of solutions for the underlying problem are investigated when the constraint set is unbounded. Moreover, a sufficient and necessary condition for ensuring the nonemptiness of the set of solutions concerned with the hemivariational inequality problem is also given.

引用

页码：1451 / 1461

页数：11

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