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

2024/10/31 by Anshika Anshika, Anshika, Anshika, Li, Jiaxing +4 · 2 citations
Computer Science · Engineering · #Matrix Theory and Algorithms #Photonic and Optical Devices

paper · pdf · doi:10.48550/arxiv.2411.00166

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.

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