# Distributed forward-backward methods for ring networks

@article{AragonArtacho2021DistributedFM, title={Distributed forward-backward methods for ring networks}, author={Francisco J. Arag'on-Artacho and Yura Malitsky and Matthew K. Tam and David Torregrosa-Bel'en}, journal={Computational Optimization and Applications}, year={2021} }

In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of the studied algorithms requires one resolvent evaluation per set-valued operator, one forward evaluation per cocoercive operator, and two forward evaluations per monotone operator. Unlike existing methods, the structure of the proposed algorithms are suitable…

## 3 Citations

### A Framework for Decentralised Resolvent Splitting

- Computer Science, Mathematics
- 2022

A new framework for decentralised resolvent splitting for solving minimisations problems with the form of a zero in the sum of set-valued monotone operators over regular networks is developed.

### Frugal and Decentralised Resolvent Splittings Defined by Nonexpansive Operators

- Mathematics, Computer ScienceArXiv
- 2022

A general framework for frugal resolvent splitting is developed which simultaneously covers and extends several important schemes in the literature and yields a new resolent splitting algorithm which is suitable for decentralised implementation on regular networks.

### Frugal Splitting Operators: Representation, Minimal Lifting and Convergence

- MathematicsArXiv
- 2022

We consider frugal splitting operators for ﬁnite sum monotone inclusion problems, i.e., splitting operators that use exactly one direct or resolvent evaluation of each operator of the sum. A novel…

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