Existence and boundedness of solutions to inclusion problems for maximal monotone vector fields in Hadamard manifolds

被引：21

作者：

Ansari, Qamrul Hasan ^{[1
,2
]}

Babu, Feeroz ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[2] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran, Saudi Arabia

来源：

OPTIMIZATION LETTERS | 2020年 / 14卷 / 03期

关键词：

Inclusion problems; Maximal monotone vector fields; Coercivity conditions; Existence results; Boundedness of solution set; Hadamard manifolds; PROXIMAL POINT ALGORITHMS; VARIATIONAL-INEQUALITIES; COERCIVITY CONDITIONS; CONVERGENCE; PROJECTION; CONVEXITY; OPERATORS; SET;

D O I：

10.1007/s11590-018-01381-x

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, we consider the inclusion problems for maximal monotone set-valued vector fields defined on Hadamard manifolds. We discuss the equivalence between nonemptiness of solution set of the inclusion problem and the coercivity condition. The boundedness of solution set of the inclusion problem is studied. An application of our results to optimization problems in Hadamard manifolds is also presented.

引用

页码：711 / 727

页数：17

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