# Shadow Douglas--Rachford Splitting for Monotone Inclusions

arXiv: https://arxiv.org/abs/1903.03393 · HTML: https://mlsanity.com/paper/1903.03393/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2019.

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

- [Beyond the Golden Ratio for Variational Inequality Algorithms](https://mlsanity.com/paper/2212.13955/) (2022)

## Abstract (arXiv)

In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a continuous dynamical system associated with the Douglas--Rachford splitting algorithm. More precisely, it is obtained by performing an explicit, rather than implicit, discretization with respect to one of the operators involved. Each iteration of the proposed algorithm requires the evaluation of one forward and one backward operator.