New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

Fixexd point theory and applications

article

Khammahawong, Konrawut¹  Kumam, Poom¹  Chaipunya, Parin¹  Plubtieng, Somyot⁴ 

[1] Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Mathematics, Faculty of Science, Naresuan University;Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University

关键词: Hadamard manifold;    Pseudomonotone vector fields;    Tseng’s extragradient method;    Variational inequality problem;   

DOI  :  10.1186/s13663-021-00689-1

来源: SpringerOpen

【 摘 要 】

We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

【 授权许可】

Unknown