# Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty

arXiv: https://arxiv.org/abs/1506.08928 · HTML: https://mlsanity.com/paper/1506.08928/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2015.

## Built on by (most cited first, 6 of 6)

- [Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2204.10607/) (2022)
- [Communication-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2110.15318/) (2021)
- [FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning](https://mlsanity.com/paper/2402.13989/) (2024)
- [Mobilizing Personalized Federated Learning in Infrastructure-Less and Heterogeneous Environments via Random Walk Stochastic ADMM](https://mlsanity.com/paper/2304.12534/) (2023)
- [DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimization](https://mlsanity.com/paper/2509.01630/) (2025)
- [Using Non-Lipschitz Signum-based Functions for Distributed Optimization and Machine Learning: Trade-off Between Con-vergence Rate and Optimality Gap](https://mlsanity.com/paper/2608.01220/) (2026)

## Abstract (arXiv)

We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of convergence by automatically deciding the constraint penalty needed for parameter consensus in each iteration. In addition, we also propose an extension of the method that adaptively determines the maximum number of iterations to update the penalty. We show that this approach effectively leads to an adaptive, dynamic network topology underlying the distributed optimization. The utility of the new penalty update schemes is demonstrated on both synthetic and real data, including a computer vision application of distributed structure from motion.