Solving Equilibrium Problem with New Inertial Technique

Abstract: We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point in the solutions set of the equilibrium problem when the associated bivariate function is pseudomonotone and satisfies Lipschitz conditions. Furthermore, in a case where the bifunction is strongly pseudomonotone, we establish a linear convergence rate. Lastly, through different numerical examples, we demonstrate that the incorporation of multiple correction terms significantly improves our proposed method when compared with other methods in the literature.