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An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems

arXiv 2507.22311 ↗First posted 30 Jul 2025math.OC cs.LGcited by 0

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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.

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References · 15

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,669
  2. 2018Federated Optimization in Heterogeneous Networkscited by 2,987
  3. 2013Distributed optimization over time-varying directed graphscited by 78
  4. 2014Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problemscited by 64
  5. 2022FedADMM: A Federated Primal-Dual Algorithm Allowing Partial Participationcited by 36
  6. 2021FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimizationcited by 29
  7. 2018Distributed Nonconvex Constrained Optimization over Time-Varying Digraphscited by 23
  8. 2017Douglas-Rachford splitting and ADMM for nonconvex optimization: tight convergence resultscited by 21
  9. 2020Federated Block Coordinate Descent Scheme for Learning Global and Personalized Modelscited by 11
  10. 2015Asynchronous Distributed ADMM for Large-Scale Optimization- Part I: Algorithm and Convergence Analysiscited by 10
  11. 2015Non-Convex Distributed Optimizationcited by 9
  12. 2019Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problemscited by 5
3 more
  1. 2023On Distributed Nonconvex Optimisation Via Modified ADMMcited by 2
  2. 2017Asynchronous ADMM for Distributed Non-Convex Optimization in Power Systemscited by 1
  3. 2018A Distributed Asynchronous Method of Multipliers for Constrained Nonconvex Optimizationcited by 1

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