# Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting

arXiv: https://arxiv.org/abs/2006.14539 · HTML: https://mlsanity.com/paper/2006.14539/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## 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)
- [Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization](https://mlsanity.com/paper/2206.03410/) (2022)
- [A Convergent ADMM Framework for Efficient Neural Network Training](https://mlsanity.com/paper/2112.11619/) (2021)
- [Constructing artificial life and materials scientists with accelerated AI using Deep AndersoNN](https://mlsanity.com/paper/2407.19724/) (2024)
- [Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification](https://mlsanity.com/paper/2410.09420/) (2024)
- [Accelerating AI Performance using Anderson Extrapolation on GPUs](https://mlsanity.com/paper/2410.19460/) (2024)

## Abstract (arXiv)

The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to converge to a solution of high-accuracy. Previously, Anderson acceleration has been applied to ADMM, by treating it as a fixed-point iteration for the concatenation of the dual variables and a subset of the primal variables. In this paper, we note that the equivalence between ADMM and Douglas-Rachford splitting reveals that ADMM is in fact a fixed-point iteration in a lower-dimensional space. By applying Anderson acceleration to such lower-dimensional fixed-point iteration, we obtain a more effective approach for accelerating ADMM. We analyze the convergence of the proposed acceleration method on nonconvex problems, and verify its effectiveness on a variety of computer graphics problems including geometry processing and physical simulation.