# The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operators

arXiv: https://arxiv.org/abs/1801.00480 · HTML: https://mlsanity.com/paper/1801.00480/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [Bregman Douglas-Rachford Splitting Method](https://mlsanity.com/paper/2509.08739/) (2025)

## Abstract (arXiv)

The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows to use r-sets-DR operators in a cyclic fashion. We prove convergence and present numerical illustrations of the potential advantage of such operators with r>2 over the classical 2-sets-DR operators in a cyclic algorithm.