# ADMM and Accelerated ADMM as Continuous Dynamical Systems

arXiv: https://arxiv.org/abs/1805.06579 · HTML: https://mlsanity.com/paper/1805.06579/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2018.

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

- [Continuous vs. Discrete Optimization of Deep Neural Networks](https://mlsanity.com/paper/2107.06608/) (2021)
- [Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents](https://mlsanity.com/paper/2203.10592/) (2022)
- [GA-HQS: MRI reconstruction via a generically accelerated unfolding approach](https://mlsanity.com/paper/2304.02883/) (2023)
- [NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer](https://mlsanity.com/paper/2209.14937/) (2022)
- [Learning by solving differential equations](https://mlsanity.com/paper/2505.13397/) (2025)
- [A General Continuous-Time Formulation of Stochastic ADMM and Its Variants](https://mlsanity.com/paper/2404.14358/) (2024)

## Abstract (arXiv)

Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by deriving the differential equations that model the continuous limit of the sequence of iterates generated by the alternating direction method of multipliers, as well as an accelerated variant. We employ the direct method of Lyapunov to analyze the stability of critical points of the dynamical systems and to obtain associated convergence rates.