# Bregman Douglas-Rachford Splitting Method

arXiv: https://arxiv.org/abs/2509.08739 · HTML: https://mlsanity.com/paper/2509.08739/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 92 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Relatively-Smooth Convex Optimization by First-Order Methods, and Applications](https://mlsanity.com/paper/1610.05708/) (2016)
- [Accelerated Bregman Proximal Gradient Methods for Relatively Smooth Convex Optimization](https://mlsanity.com/paper/1808.03045/) (2018)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Bregman Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1306.3203/) (2013)
- [Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems](https://mlsanity.com/paper/1409.8444/) (2014)
- [Bregman Forward-Backward Operator Splitting](https://mlsanity.com/paper/1908.03878/) (2019)
- [Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants](https://mlsanity.com/paper/1806.03430/) (2018)
- [Bregman Augmented Lagrangian and Its Acceleration](https://mlsanity.com/paper/2002.06315/) (2020)
- [On the Douglas-Rachford algorithm](https://mlsanity.com/paper/1604.04603/) (2016)
- [Survey: Sixty Years of Douglas--Rachford](https://mlsanity.com/paper/1809.07181/) (2018)
- [The Douglas--Rachford Algorithm Converges Only Weakly](https://mlsanity.com/paper/1912.09564/) (2019)
- [The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operators](https://mlsanity.com/paper/1801.00480/) (2018)
- [Douglas--Rachford Splitting and ADMM for Pathological Convex Optimization](https://mlsanity.com/paper/1801.06618/) (2018)
- [Uniqueness of DRS as the 2 Operator Resolvent-Splitting and Impossibility of 3 Operator Resolvent-Splitting](https://mlsanity.com/paper/1802.07534/) (2018)

## Built on by (most cited first, 2 of 2)

- [Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory](https://mlsanity.com/paper/2609.33814/) (2026)
- [GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport](https://mlsanity.com/paper/2610.04715/) (2026)

## Abstract (arXiv)

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.