Two step inertial Tseng method for solving monotone variational inclusion problem

Abstract

In this paper, we examine the monotone variational inclusion problem with a maximal monotone operator and a Lipschitz continuous monotone operator. We propose two different iterative algorithms for solving the monotone variational inclusion problem, utilizing a new self-adaptive step size and a two-step inertial technique. Under the assumption that the solution set of the monotone variational inclusion problem is nonempty, we prove weak and strong convergence theorems concerning the sequences generated by our proposed algorithms. The convergence is guaranteed under some mild assumptions. Some numerical experiments are presented to demonstrate the performance of our iterative algorithms in comparison with recent results in the literature.