Variable Metric Forward-Backward Splitting with Applications to Monotone Inclusions in Duality

TL;DR

This paper introduces a variable metric forward-backward splitting algorithm with proven convergence, and applies it to develop new primal-dual algorithms for monotone inclusions, broadening the scope of existing methods.

Contribution

It proposes a novel variable metric forward-backward splitting framework and derives new primal-dual algorithms for monotone inclusions, including special cases.

Findings

Proven convergence of the proposed algorithm in Hilbert spaces

Development of new primal-dual splitting algorithms

Application to various classes of monotone inclusions

Abstract

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed.