A self-adaptive parallel subgradient extragradient method for finite family of pseudomonotone equilibrium and fixed point problems

In this paper, we introduce a self-adaptive parallel subgradient extragradient method for solving a finite family of pseudomonotone equilibrium problem and common fixed point problems in real Hilbert spaces. The algorithm is designed such that its stepsize is determined by a self-adaptive process and a convex combination method is used to approximate the sequences generated by the strongly convex optimization problems. This improves the convergence of the method and also avoids the need for choosing prior estimate of the Lipschitz-like constants of the bifunctions. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed method to the desired solution. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.