# An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems

arXiv: https://arxiv.org/abs/2507.22311 · HTML: https://mlsanity.com/paper/2507.22311/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [FedADMM: A Federated Primal-Dual Algorithm Allowing Partial Participation](https://mlsanity.com/paper/2203.15104/) (2022)
- [FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimization](https://mlsanity.com/paper/2103.03452/) (2021)
- [Distributed Nonconvex Constrained Optimization over Time-Varying Digraphs](https://mlsanity.com/paper/1809.01106/) (2018)
- [Douglas-Rachford splitting and ADMM for nonconvex optimization: tight convergence results](https://mlsanity.com/paper/1709.05747/) (2017)
- [Federated Block Coordinate Descent Scheme for Learning Global and Personalized Models](https://mlsanity.com/paper/2012.13900/) (2020)
- [Asynchronous Distributed ADMM for Large-Scale Optimization- Part I: Algorithm and Convergence Analysis](https://mlsanity.com/paper/1509.02597/) (2015)
- [Non-Convex Distributed Optimization](https://mlsanity.com/paper/1512.00895/) (2015)
- [Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems](https://mlsanity.com/paper/1906.10053/) (2019)
- [On Distributed Nonconvex Optimisation Via Modified ADMM](https://mlsanity.com/paper/2312.03958/) (2023)
- [Asynchronous ADMM for Distributed Non-Convex Optimization in Power Systems](https://mlsanity.com/paper/1710.08938/) (2017)
- [A Distributed Asynchronous Method of Multipliers for Constrained Nonconvex Optimization](https://mlsanity.com/paper/1806.05181/) (2018)

## Abstract (arXiv)

In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents in the network to distributedly and asynchronously compute a set of first-order stationary solutions of the problem. To the best of our knowledge, this is the first decentralised and asynchronous algorithm for solving nonconvex optimisation problems with convergence proof. The numerical examples demonstrate the efficiency of the proposed algorithm for distributed Phase Retrieval and sparse Principal Component Analysis problems.