A variable metric extension of the forward--backward--forward algorithm for monotone operators

TL;DR

This paper introduces a variable metric extension of the forward-backward-forward algorithm to efficiently solve monotone operator problems in Hilbert spaces, unifying and generalizing existing splitting methods.

Contribution

It presents a novel variable metric framework that extends the forward-backward-forward algorithm for monotone inclusions, encompassing several recent algorithms as special cases.

Findings

The proposed algorithm converges under broad conditions.

It unifies multiple existing splitting algorithms.

It effectively handles sums of composite operators.

Abstract

We propose a variable metric extension of the forward--backward-forward algorithm for finding a zero of the sum of a maximally monotone operator and a Lipschitzian monotone operator in Hilbert spaces. In turn, this framework provides a variable metric splitting algorithm for solving monotone inclusions involving sums of composite operators. Several splitting algorithms recently proposed in the literature are recovered as special cases.