# Non-stationary Douglas-Rachford and alternating direction method of multipliers: adaptive stepsizes and convergence

arXiv: https://arxiv.org/abs/1801.03765 · HTML: https://mlsanity.com/paper/1801.03765/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2018.

## Built on by (most cited first, 3 of 3)

- [Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions](https://mlsanity.com/paper/2110.08150/) (2021)
- [On the Expressive Power of GNNs to Solve Linear SDPs](https://mlsanity.com/paper/2604.27786/) (2026)
- [HETA++: Global Structure-from-Motion with Hybrid Explicit Translation Averaging](https://mlsanity.com/paper/2607.15912/) (2026)

## Abstract (arXiv)

We revisit the classical Douglas-Rachford (DR) method for finding a zero of the sum of two maximal monotone operators. Since the practical performance of the DR method crucially depends on the stepsizes, we aim at developing an adaptive stepsize rule. To that end, we take a closer look at a linear case of the problem and use our findings to develop a stepsize strategy that eliminates the need for stepsize tuning. We analyze a general non-stationary DR scheme and prove its convergence for a convergent sequence of stepsizes with summable increments. This, in turn, proves the convergence of the method with the new adaptive stepsize rule. We also derive the related non-stationary alternating direction method of multipliers (ADMM) from such a non-stationary DR method. We illustrate the efficiency of the proposed methods on several numerical examples.