On quasi-inertial double extragradient-type iterations for variational inequalities and Bregman relatively asymptotically nonexpansive mapping

Abstract

This paper introduces two quasi-inertial double extragradient-type algorithms with an inexact line search process to solve a pair of pseudomonotone variational inequality problems constrained by a common fixed point problem in a Banach space characterized by both p-uniform convexity and uniform smoothness. The common fixed point constraint of the problem is given by a Bregman relatively asymptotically nonexpansive mapping and finitely many Bregman relatively nonexpansive mappings. With mild restrictions in place, we establish both weak and strong convergence of the proposed algorithms toward a common solution for the two pseudomonotone variational inequality problems with the CFPP constraint, respectively. Finally, we illustrate the effectiveness and applicability of our proposed methods through multiple numerical tests. In the numerical experiments, we analyze the effect of the selected parameters on the performance of the proposed algorithms. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.