# Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration

arXiv: https://arxiv.org/abs/1906.10114 · HTML: https://mlsanity.com/paper/1906.10114/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2019.

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

- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [Bringing regularized optimal transport to lightspeed: a splitting method adapted for GPUs](https://mlsanity.com/paper/2305.18483/) (2023)
- [Training Generative Adversarial Networks with Adaptive Composite Gradient](https://mlsanity.com/paper/2111.05508/) (2021)
- [Anderson acceleration for iteratively reweighted ℓ1 algorithm](https://mlsanity.com/paper/2403.07271/) (2024)
- [A General Continuous-Time Formulation of Stochastic ADMM and Its Variants](https://mlsanity.com/paper/2404.14358/) (2024)
- [A Double Inertial Forward-Backward Splitting Algorithm With Applications to Regression and Classification Problems](https://mlsanity.com/paper/2505.03794/) (2025)

## Abstract (arXiv)

The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to improve the performance of the method, such as the inertial technique. By studying the geometric properties of ADMM, we discuss the limitations of current inertial accelerated ADMM and then present and analyze an adaptive acceleration scheme for the method. Numerical experiments on problems arising from image processing, statistics and machine learning demonstrate the advantages of the proposed acceleration approach.