Convergence theorems for solving a system of pseudomonotone variational inequalities using Bregman distance in Banach spaces

In this paper, we present two new parallel Bregman projection algorithms for finding a common solution of a system of pseudomonotone variational inequality problems in a real reflexive Banach space. The first algorithm combines a parallel Bregman subgradient extragradient method with the Halpern iterative method for approximating a common solution of variational inequalities in reflexive Banach spaces. The second algorithm involves a parallel Bregman subgradient extragradient method, Halpern iterative method and a line search procedure which aims to avoid the condition of finding prior estimate of the Lipschitz constant of each cost operator. Two strong convergence results were proved under standard assumptions imposed on the cost operators and control sequences. Finally, we provide some numerical experiments to illustrate the behaviour of the sequences generated by the proposed algorithms.