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arXiv · 2411.00166

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

Anshika Anshika·Jiaxing Li·Debdas Ghosh·Xiangxiong Zhang
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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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Anshika Anshika, Jiaxing Li, Debdas Ghosh, Xiangxiong Zhang. 2024-10-31. A Three-Operator Splitting Scheme Derived from Three-Block ADMM. https://arxiv.org/abs/2411.00166

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