Variable metric algorithms driven by averaged operators

TL;DR

This paper introduces a new variable metric algorithm based on averaged operators, proving its convergence and demonstrating applications to monotone operator splitting.

Contribution

It presents a novel variable metric algorithm leveraging compositions of averaged operators, with proven convergence and practical applications.

Findings

Convergence of the proposed algorithm is established.

Applications to monotone operator splitting are demonstrated.

The method offers a flexible framework for operator splitting problems.

Abstract

The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.