# Finding the forward-Douglas-Rachford-forward method

arXiv: https://arxiv.org/abs/1909.09747 · HTML: https://mlsanity.com/paper/1909.09747/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2019.

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

- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)

## Abstract (arXiv)

We consider the monotone inclusion problem with a sum of 3 operators, in which 2 are monotone and 1 is monotone-Lipschitz. The classical Douglas--Rachford and Forward-backward-forward methods respectively solve the monotone inclusion problem with a sum of 2 monotone operators and a sum of 1 monotone and 1 monotone-Lipschitz operators. We first present a method that naturally combines Douglas--Rachford and Forward-backward-forward and show that it solves the 3 operator problem under further assumptions, but fails in general. We then present a method that naturally combines Douglas--Rachford and forward-reflected-backward, a recently proposed alternative to Forward-backward-forward by Malitsky and Tam [arXiv:1808.04162, 2018]. We show that this second method solves the 3 operator problem generally, without further assumptions.