mlsanityData to 14 Oct 2026

On the Linear Convergence of the ADMM in Decentralized Consensus Optimization

arXiv 1307.5561 ↗First posted 21 Jul 2013math.OCcited by 57

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Abstract (arXiv)

In decentralized consensus optimization, a connected network of agents collaboratively minimize the sum of their local objective functions over a common decision variable, where their information exchange is restricted between the neighbors. To this end, one can first obtain a problem reformulation and then apply the alternating direction method of multipliers (ADMM). The method applies iterative computation at the individual agents and information exchange between the neighbors. This approach has been observed to converge quickly and deemed powerful. This paper establishes its linear convergence rate for decentralized consensus optimization problem with strongly convex local objective functions. The theoretical convergence rate is explicitly given in terms of the network topology, the properties of local objective functions, and the algorithm parameter. This result is not only a performance guarantee but also a guideline toward accelerating the ADMM convergence.

Key facts. Cited by 57 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Jul 2013.

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Citing papers per year: 2021: 11; 2022: 14; 2023: 15; 2024: 6; 2025: 6; 2026: 5.

57 papers.

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  1. 2022Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challengescited by 138
  2. 2021Semi-Decentralized Federated Learning with Cooperative D2D Local Model Aggregationscited by 51
  3. 2021Decentralized Riemannian Gradient Descent on the Stiefel Manifoldcited by 33
  4. 2021Removing Data Heterogeneity Influence Enhances Network Topology Dependence of Decentralized SGDcited by 29
  5. 2021Accelerating Gossip SGD with Periodic Global Averagingcited by 25
  6. 2022Communication-Efficient Topologies for Decentralized Learning with O(1) Consensus Ratecited by 25
  7. 2022Revisiting Optimal Convergence Rate for Smooth and Non-convex Stochastic Decentralized Optimizationcited by 23
  8. 2021BlueFog: Make Decentralized Algorithms Practical for Optimization and Deep Learningcited by 16
  9. 2022Networked Signal and Information Processingcited by 10
  10. 2022Decentralized Nonconvex Optimization with Guaranteed Privacy and Accuracycited by 10
  11. 2022Confederated Learning: Federated Learning with Decentralized Edge Serverscited by 7
  12. 2023Advancements in Federated Learning: Models, Methods, and Privacycited by 7
38 more
  1. 2023Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifoldcited by 7
  2. 2023Stochastic Unrolled Federated Learningcited by 6
  3. 2023DSGD-CECA: Decentralized SGD with Communication-Optimal Exact Consensus Algorithmcited by 6
  4. 2022Federated Stochastic Primal-dual Learning with Differential Privacycited by 5
  5. 2022DR-DSGD: A Distributionally Robust Decentralized Learning Algorithm over Graphscited by 5
  6. 2022DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimizationcited by 5
  7. 2023Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimizationcited by 5
  8. 2023From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learningcited by 5
  9. 2022Communication Efficient Federated Learning via Ordered ADMM in a Fully Decentralized Settingcited by 4
  10. 2022Fast and Robust Sparsity Learning over Networks: A Decentralized Surrogate Median Regression Approachcited by 4
  11. 2022Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learningcited by 4
  12. 2023Personalized Graph Federated Learning with Differential Privacycited by 4
  13. 2025Distributed Conformal Prediction via Message Passingcited by 4
  14. 2025From Centralized to Decentralized Federated Learning: Theoretical Insights, Privacy Preservation, and Robustness Challengescited by 4
  15. 2021Decentralized Multi-Task Stochastic Optimization With Compressed Communicationscited by 3
  16. 2023Mobilizing Personalized Federated Learning in Infrastructure-Less and Heterogeneous Environments via Random Walk Stochastic ADMMcited by 3
  17. 2021Transient growth of accelerated optimization algorithmscited by 2
  18. 2022A Penalty-Based Method for Communication-Efficient Decentralized Bilevel Programmingcited by 2
  19. 2023Limited Communications Distributed Optimization via Deep Unfolded Distributed ADMMcited by 2
  20. 2024Quantization Avoids Saddle Points in Distributed Optimizationcited by 2
  21. 2024Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approachcited by 2
  22. 2021Distributed Sparse Regression via Penalizationcited by 1
  23. 2021Decentralized Stochastic Proximal Gradient Descent with Variance Reduction over Time-varying Networkscited by 1
  24. 2022Asynchronous Parallel Incremental Block-Coordinate Descent for Decentralized Machine Learningcited by 1
  25. 2023Decentralized Entropic Optimal Transport for Distributed Distribution Comparisoncited by 1
  26. 2023Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensuscited by 1
  27. 2023Generalizing Differentially Private Decentralized Deep Learning with Multi-Agent Consensuscited by 1
  28. 2025Enhancing Parallelism in Decentralized Stochastic Convex Optimizationcited by 1
  29. 2025Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Trackingcited by 1
  30. 2025Distributed optimization: designed for federated learningcited by 1
  31. 2025Large Language Model-Assisted Planning of Electric Vehicle Charging Infrastructure with Real-World Case Studycited by 1
  32. 2026Accelerated Decentralized Stochastic Gradient Descent for Strongly Convex Optimizationcited by 1
  33. 2021Adaptive Stochastic ADMM for Decentralized Reinforcement Learning in Edge Industrial IoTcited by 0
  34. 2021Random Graph-Based Neuromorphic Learning with a Layer-Weaken Structurecited by 0
  35. 2023Differentially Private Distributed Convex Optimizationcited by 0
  36. 2023Private Networked Federated Learning for Nonsmooth Objectivescited by 0
  37. 2023On Linear Convergence of PI Consensus Algorithm under the Restricted Secant Inequalitycited by 0
  38. 2024Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multiplierscited by 0

50 most cited of 57 All 57 (JSON)