The variable metric three-operator algorithms for solving monotone inclusions

Abstract

In this paper, we propose an inexact variable metric three-operator algorithm and a viscous version of it for finding a zero of the sum of three monotone operators in a real Hilbert space. Under some appropriate conditions, we establish the weak or strong convergence of the proposed algorithms. As a special case of the proposed problem, we present a variable metric Douglas–Rachford splitting algorithm and obtain a strong convergence result. The algorithms and the results in this paper are further extensions of the algorithms and results for solving the zero inclusion problems of monotone operators. To illustrate the efficiency of the proposed algorithms, we construct the numerical experiments and give some choices for the variable metric matrix.