A Three-Operator Splitting Scheme Derived from Three-Block ADMM

TL;DR

This paper introduces a novel three-operator splitting method extending Douglas-Rachford techniques to three operators, demonstrating robustness and convergence properties for convex optimization problems involving three functions.

Contribution

It proposes a new three-operator splitting scheme for monotone inclusion and convex optimization, extending existing methods like Davis-Yin splitting and three-block ADMM.

Findings

The splitting scheme is robust with larger step sizes.

When two functions have orthogonal domains, the operator is 1/2-averaged.

The method guarantees convergence under certain conditions.

Abstract

This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems involving three operators. For solving a composite convex minimization of a sum of three functions, its formula resembles but is different from Davis-Yin splitting and the dual formulation of the classical three-block ADMM. Numerical tests suggest that such a splitting scheme is robust in the sense of allowing larger step sizes. When two functions have orthogonal domains, the splitting operator can be proven 1/2-averaged, which implies convergence of the iteration scheme using any positive step size.