Modified forward-backward-forward Bregman projection method to solve quasi-monotone variational inequalities and fixed point problems in reflexive Banach spaces

This paper is concerned with the common solution of quasimonotone variational inequalities and fixed-point problems in reflexive Banach spaces. We introduce a novel forward-backward-forward Bregman projection method that incorporates inertial-like effects. Our proposed method eliminates the need for any line search rules. Instead, it employs a more efficient and intelligent nonmonotone adaptive step size, which the growth rate can be adjusted adaptively through the setting control series. Furthermore, we demonstrate that our proposed algorithm converges strongly and analyse its convergence rate under certain suitable conditions. This algorithm is applicable for solving network traffic distribution models as well as convex constrained optimization problems. Finally, we validate the efficiency and feasibility of our proposed algorithms through numerical experiments and simulations related to image deblurring problems.