Almost sure convergence of the forward-backward-forward splitting algorithm

TL;DR

This paper introduces a stochastic forward-backward-forward splitting algorithm and proves its almost sure weak convergence in Hilbert spaces, with applications to composite monotone inclusion and minimization problems.

Contribution

It presents a novel stochastic splitting algorithm with proven convergence properties for complex optimization problems.

Findings

Proved almost sure weak convergence of the algorithm.

Demonstrated applications to monotone inclusion problems.

Validated effectiveness through theoretical analysis.

Abstract

In this paper, we propose a stochastic forward-backward-forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are demonstrated.