# Douglas-Rachford Splitting: Complexity Estimates and Accelerated Variants

arXiv: https://arxiv.org/abs/1407.6723 · HTML: https://mlsanity.com/paper/1407.6723/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2014.

## Built on by (most cited first, 4 of 4)

- [Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions](https://mlsanity.com/paper/2110.08150/) (2021)
- [PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python](https://mlsanity.com/paper/2201.04040/) (2022)
- [Accelerated forward-backward and Douglas-Rachford splitting dynamics](https://mlsanity.com/paper/2407.20620/) (2024)
- [Robust Non-negative Proximal Gradient Algorithm for Inverse Problems](https://mlsanity.com/paper/2510.23362/) (2025)

## Abstract (arXiv)

We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope (DRE), whose stationary points correspond to the solutions of the original (possibly nonsmooth) problem. By proving the equivalence between the Douglas-Rachford splitting method and a scaled gradient method applied to the DRE, results from smooth unconstrained optimization are employed to analyze convergence properties of DRS, to tune the method and to derive an accelerated version of it.