# Bregman Alternating Direction Method of Multipliers

arXiv: https://arxiv.org/abs/1306.3203 · HTML: https://mlsanity.com/paper/1306.3203/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2013.

## Built on by (most cited first, 19 of 19)

- [Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotion](https://mlsanity.com/paper/2210.10044/) (2022)
- [Towards Compositional Adversarial Robustness: Generalizing Adversarial Training to Composite Semantic Perturbations](https://mlsanity.com/paper/2202.04235/) (2022)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing](https://mlsanity.com/paper/2207.02087/) (2022)
- [Federated Learning Using Three-Operator ADMM](https://mlsanity.com/paper/2211.04152/) (2022)
- [Federated ADMM from Bayesian Duality](https://mlsanity.com/paper/2506.13150/) (2025)
- [A Provably Convergent Information Bottleneck Solution via ADMM](https://mlsanity.com/paper/2102.04729/) (2021)
- [Regularized Optimal Transport Layers for Generalized Global Pooling Operations](https://mlsanity.com/paper/2212.06339/) (2022)
- [Machine Learning Meets Advanced Robotic Manipulation](https://mlsanity.com/paper/2309.12560/) (2023)
- [Bregman Douglas-Rachford Splitting Method](https://mlsanity.com/paper/2509.08739/) (2025)
- [Decentralized Entropic Optimal Transport for Distributed Distribution Comparison](https://mlsanity.com/paper/2301.12065/) (2023)
- [A Quasi-Wasserstein Loss for Learning Graph Neural Networks](https://mlsanity.com/paper/2310.11762/) (2023)
- [LAGO: Few-shot Crosslingual Embedding Inversion Attacks via Language Similarity-Aware Graph Optimization](https://mlsanity.com/paper/2505.16008/) (2025)
- [Hawkes Processes on Graphons](https://mlsanity.com/paper/2102.02741/) (2021)
- [Revisiting Global Pooling through the Lens of Optimal Transport](https://mlsanity.com/paper/2201.09191/) (2022)
- [Symmetrizing Bregman Divergence on the Cone of Positive Definite Matrices: Which Mean to Use and Why](https://mlsanity.com/paper/2603.28917/) (2026)
- [Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization](https://mlsanity.com/paper/2606.28307/) (2026)
- [Optimal transport meets speech: a tutorial review](https://mlsanity.com/paper/2609.31787/) (2026)

## Abstract (arXiv)

The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit the structure of problems. BADMM provides a unified framework for ADMM and its variants, including generalized ADMM, inexact ADMM and Bethe ADMM. We establish the global convergence and the O(1/T) iteration complexity for BADMM. In some cases, BADMM can be faster than ADMM by a factor of O(n/log(n)). In solving the linear program of mass transportation problem, BADMM leads to massive parallelism and can easily run on GPU. BADMM is several times faster than highly optimized commercial software Gurobi.