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<p>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.</p>

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A three-operator splitting scheme derived from three-block ADMM

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月19日

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  • Anshika Anshika,
  • Jiaxing Li,
  • Debdas Ghosh,
  • Xiangxiong Zhang

摘要

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.