New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds
Konrawut Khammahawong, Poom Kumam, Parin Chaipunya, Somyot Plubtieng · Fixed Point Theory and Algorithms for Sciences and Engineering · 2021
Abstract 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.