An Inertial Iterative Algorithm for Approximating Common Solutions to Split Equalities of Some Nonlinear Optimization Problems

Abstract

In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.