Two-step inertial forward–reflected–anchored–backward splitting algorithm for solving monotone inclusion problems

Abstract

The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of Malitsky and Tam in a real Hilbert space. Our proposed algorithm converges strongly to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. It involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. Finally, we perform numerical experiments involving image restoration problem and compare our algorithm with known related strongly convergent splitting algorithms in the literature.