# Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM

arXiv: https://arxiv.org/abs/1410.8479 · HTML: https://mlsanity.com/paper/1410.8479/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2014.

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

- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [OKRidge: Scalable Optimal k-Sparse Ridge Regression](https://mlsanity.com/paper/2304.06686/) (2023)
- [OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression](https://mlsanity.com/paper/2105.13271/) (2021)
- [Theoretical Analysis of Primal-Dual Algorithm for Non-Convex Stochastic Decentralized Optimization](https://mlsanity.com/paper/2205.11979/) (2022)

## Abstract (arXiv)

Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods.