An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems

• URL: http://arxiv.org/abs/2507.22311v1
• Date: Wed, 30 Jul 2025 00:55:17 GMT
• Title: An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems
• Authors: Behnam Mafakheri, Jonathan H. Manton, Iman Shames,
• Abstract summary: In this paper, we consider non decentralised optimisation and a network of distributed agents.<n>We develop an ADMM algorithm based on the Randomised.<n>Douglas.<n>Rachford Block agents.
• Score: 3.2689702143620147
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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