Bregman Douglas-Rachford Splitting Method

Shiqian Ma; Lin Xiao; Renbo Zhao

doi:10.48550/arxiv.2509.08739

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Bregman Douglas-Rachford Splitting Method

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Bregman Douglas-Rachford Splitting Method

Shiqian Ma, Lin Xiao and Renbo Zhao

ArXiv.org

Cornell University

09/10/2025

DOI: 10.48550/arxiv.2509.08739

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https://doi.org/10.48550/arxiv.2509.08739View

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Abstract

In this paper, we propose the Bregman Douglas-Rachford splitting (BDRS) method and its variant Bregman Peaceman-Rachford splitting method for solving maximal monotone inclusion problem. We show that BDRS is equivalent to a Bregman alternating direction method of multipliers (ADMM) when applied to the dual of the problem. A special case of the Bregman ADMM is an alternating direction version of the exponential multiplier method. To the best of our knowledge, algorithms proposed in this paper are new to the literature. We also discuss how to use our algorithms to solve the discrete optimal transport (OT) problem. We prove the convergence of the algorithms under certain assumptions, though we point out that one assumption does not apply to the OT problem.

Computer Science - Learning

Mathematics - Optimization and Control

Statistics - Machine Learning

Details

Title: Subtitle: Bregman Douglas-Rachford Splitting Method
Creators: Shiqian Ma
Lin Xiao
Renbo Zhao
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2509.08739
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 09/10/2025
Academic Unit: Business Analytics
Record Identifier: 9984962538502771

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