Bregman Douglas-Rachford Splitting Method
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.
Cite
@article{arxiv.2509.08739,
title = {Bregman Douglas-Rachford Splitting Method},
author = {Shiqian Ma and Lin Xiao and Renbo Zhao},
journal= {arXiv preprint arXiv:2509.08739},
year = {2025}
}