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arXiv · 2605.17731

A reflected forward-backward splitting algorithmic framework

Haowen Zheng·Yongyu Fu·Qiao-Li Dong·Shuangbao Li
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Abstract

In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddle-point problem is then presented to demonstrate the effectiveness of the proposed algorithm.

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Haowen Zheng, Yongyu Fu, Qiao-Li Dong, Shuangbao Li. 2026-05-18. A reflected forward-backward splitting algorithmic framework. https://arxiv.org/abs/2605.17731

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