# Convergence of Bregman alternating direction method with multipliers for nonconvex composite problems

arXiv: https://arxiv.org/abs/1410.8625 · HTML: https://mlsanity.com/paper/1410.8625/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2014.

## Built on by (most cited first, 7 of 7)

- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [AugFL: Augmenting Federated Learning with Pretrained Models](https://mlsanity.com/paper/2503.02154/) (2025)
- [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)
- [SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inference](https://mlsanity.com/paper/2602.00942/) (2026)
- [Differentiable Projection-based Learn to Optimize in Wireless Network-Part I: Convex Constrained (Non-)Convex Programming](https://mlsanity.com/paper/2502.00053/) (2025)
- [Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization](https://mlsanity.com/paper/2606.28307/) (2026)

## Abstract (arXiv)

The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various convex or nonconvex composite problems that arise in the fields of image & signal processing and machine learning. In convex settings, numerous convergence results have been established for ADMM as well as its varieties. However, due to the absence of convexity, the convergence analysis of nonconvex ADMM is generally very difficult. In this paper we study the Bregman modification of ADMM (BADMM), which includes the conventional ADMM as a special case and often leads to an improvement of the performance of the algorithm. Under certain assumptions, we prove that the iterative sequence generated by BADMM converges to a stationary point of the associated augmented Lagrangian function. The obtained results underline the feasibility of ADMM in applications under nonconvex settings.