# Anderson Accelerated Douglas-Rachford Splitting

arXiv: https://arxiv.org/abs/1908.11482 · HTML: https://mlsanity.com/paper/1908.11482/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2019.

## Built on by (most cited first, 8 of 8)

- [DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting](https://mlsanity.com/paper/2106.09117/) (2021)
- [Damped Anderson Mixing for Deep Reinforcement Learning: Acceleration, Convergence, and Stabilization](https://mlsanity.com/paper/2110.08896/) (2021)
- [An Operator Splitting View of Federated Learning](https://mlsanity.com/paper/2108.05974/) (2021)
- [Anderson Acceleration For Bioinformatics-Based Machine Learning](https://mlsanity.com/paper/2302.00347/) (2023)
- [Anderson Acceleration as a Krylov Method with Application to Asymptotic Convergence Analysis](https://mlsanity.com/paper/2109.14181/) (2021)
- [Anderson acceleration for iteratively reweighted ℓ1 algorithm](https://mlsanity.com/paper/2403.07271/) (2024)
- [Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification](https://mlsanity.com/paper/2410.09420/) (2024)
- [Designing across domains with declarative thinking: Insights from the 96-Eyes ptychographic imager project](https://mlsanity.com/paper/2508.18512/) (2025)

## Abstract (arXiv)

We consider the problem of non-smooth convex optimization with linear equality constraints, where the objective function is only accessible through its proximal operator. This problem arises in many different fields such as statistical learning, computational imaging, telecommunications, and optimal control. To solve it, we propose an Anderson accelerated Douglas-Rachford splitting (A2DR) algorithm, which we show either globally converges or provides a certificate of infeasibility/unboundedness under very mild conditions. Applied to a block separable objective, A2DR partially decouples so that its steps may be carried out in parallel, yielding an algorithm that is fast and scalable to multiple processors. We describe an open-source implementation and demonstrate its performance on a wide range of examples.