Forward-Backward Splitting with Bregman Distances

TL;DR

This paper introduces a forward-backward splitting algorithm utilizing Bregman distances for solving composite minimization problems in reflexive Banach spaces, with proven convergence and new algorithmic variants in Euclidean spaces.

Contribution

It develops a novel forward-backward splitting method based on Bregman distances, extending applicability to general Banach spaces and providing convergence analysis.

Findings

Convergence of the proposed algorithm is established.

New algorithms are derived for Euclidean spaces.

The method applies to a broad class of composite minimization problems.

Abstract

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained.