mlsanityData to 14 Oct 2026

Bregman Douglas-Rachford Splitting Method

arXiv 2509.08739 ↗First posted 10 Sep 2025math.OC cs.LG stat.MLcited by 2

Not on the map. Why?

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.

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

15 of 92 references.

References · 15

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2016Relatively-Smooth Convex Optimization by First-Order Methods, and Applicationscited by 108
  3. 2018Accelerated Bregman Proximal Gradient Methods for Relatively Smooth Convex Optimizationcited by 20
  4. 2013Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problemscited by 19
  5. 2013Bregman Alternating Direction Method of Multiplierscited by 19
  6. 2014Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problemscited by 15
  7. 2019Bregman Forward-Backward Operator Splittingcited by 7
  8. 2018Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variantscited by 5
  9. 2020Bregman Augmented Lagrangian and Its Accelerationcited by 3
  10. 2016On the Douglas-Rachford algorithmcited by 2
  11. 2018Survey: Sixty Years of Douglas--Rachfordcited by 2
  12. 2019The Douglas--Rachford Algorithm Converges Only Weaklycited by 2
3 more
  1. 2018The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operatorscited by 1
  2. 2018Douglas--Rachford Splitting and ADMM for Pathological Convex Optimizationcited by 1
  3. 2018Uniqueness of DRS as the 2 Operator Resolvent-Splitting and Impossibility of 3 Operator Resolvent-Splittingcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memorycited by 0
  2. 2026GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transportcited by 0