# Accelerating ADMM for Efficient Simulation and Optimization

arXiv: https://arxiv.org/abs/1909.00470 · HTML: https://mlsanity.com/paper/1909.00470/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2019.

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

- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization](https://mlsanity.com/paper/2206.03410/) (2022)
- [DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting](https://mlsanity.com/paper/2106.09117/) (2021)
- [Advancements in Federated Learning: Models, Methods, and Privacy](https://mlsanity.com/paper/2302.11466/) (2023)
- [Superpixel-guided Discriminative Low-rank Representation of Hyperspectral Images for Classification](https://mlsanity.com/paper/2108.11172/) (2021)
- [Learning to accelerate distributed ADMM using graph neural networks](https://mlsanity.com/paper/2509.05288/) (2025)
- [A Convergent ADMM Framework for Efficient Neural Network Training](https://mlsanity.com/paper/2112.11619/) (2021)

## Abstract (arXiv)

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.