An extragradient method for non-monotone equilibrium problems on Hadamard manifolds with applications

被引：11

作者：

Babu, Feeroz ^{[1
]}

Ali, Akram ^{[2
,3
]}

Alkhaldi, Ali H. ^{[2
]}

机构：

[1] Aligarh Muslim Univ, ZH Coll Engn & Technol, Dept Appl Math, Aligarh 202002, India

[2] King Khalid Univ, Coll Sci, Dept Math, Abha 9004, Saudi Arabia

[3] Univ Fed Amazonas, Dept Matemat, UFAM, BR-69080900 Manaus, AM, Brazil

来源：

APPLIED NUMERICAL MATHEMATICS | 2022年 / 180卷

关键词：

Equilibrium problems; Minty equilibrium problems; Convex; Hadamard manifolds; Nash equilibrium; PROXIMAL POINT ALGORITHM; MONOTONE VECTOR-FIELDS; VARIATIONAL-INEQUALITIES; RIEMANNIAN-MANIFOLDS; INCLUSION PROBLEMS; NASH EQUILIBRIA; PROJECTION; EXISTENCE; VERIFICATION; CONVEX;

D O I：

10.1016/j.apnum.2022.05.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we consider a non-monotone equilibrium problem on Hadamard manifolds and define Armijo's type extragradient algorithm for the proposed equilibrium problem. The introduced algorithm does not require objective bifunction's monotonicity and the solution set's nonemptiness. A convergence result of our algorithm under very mild assumptions is presented. Moreover, we investigate the applications of the established results to the non-monotone set-valued variational inequalities and the generalized Nash equilibrium problems from the considered method. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：85 / 103

页数：19

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