New General Fixed-Point Approach to Compute the Resolvent of Composite Operators

TL;DR

This paper introduces a new fixed-point method for efficiently computing the resolvent of composite operators, with proven convergence properties and advantages over existing techniques.

Contribution

The paper presents a novel, stable fixed-point algorithm for resolvent computation of composite maximal monotone operators, with comprehensive convergence analysis.

Findings

Weak, strong, and linear convergence established.

Method demonstrates advantages over existing approaches.

Applicable to a broad class of composite operators.

Abstract

In this paper, we propose a new general and stable fixed-point approach to compute the resolvents of the composition of a set-valued maximal monotone operator with a linear bounded mapping. Weak, strong and linear convergence of the proposed algorithms are obtained. Advantages of our method over the existing approaches are also thoroughly analyzed.