Relaxed Inertial Subgradient Extragradient Algorithm for Solving Equilibrium Problems

Abstract We propose a relaxed inertial subgradient extragradient algorithm for solving equilibrium problems in a real Hilbert space. Under the assumption that the associated bivariate function is pseudomonotone and satisfies the Lipschitzness, we establish that the generated sequence of our proposed algorithm converges weakly to the equilibria set of the equilibrium problem. Furthermore, we obtain a linear convergence rate under the assumption that the bifunction is strongly pseudomonotone. We apply our proposed algorithm to variational inequality and fixed point problems. Finally, we compare our method with other schemes in the literature and the improvement brought by our proposed method is evident in the numerical experiments considered in this paper.