Convergence analysis of Bregman projection methods with a new extrapolation technique for solving variational inequalities in reflexive Banach spaces

Abstract.

In this paper, we firstly propose a Bregman projection algorithm with a new
extrapolation technique for solving quasi-monotone variational inequalities in reflexive Banach spaces. We establish the weak convergence and non-asymptotic convergence rate of the algorithm under appropriate and mild assumptions. Secondly, we introduce the second algorithm and demonstrate its linear convergence under stronger conditions. Our numerical experiments show that our methods outperform existing algorithms in the literature.