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A General Analysis of the Convergence of ADMM

arXiv 1502.02009 ↗First posted 6 Feb 2015math.OC cs.NA math.NAcited by 22

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Abstract (arXiv)

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms introduced in Lessard et al. (2014), reducing algorithm convergence to verifying the stability of a dynamical system. This approach generalizes a number of existing results and obviates any assumptions about specific choices of algorithm parameters. On a numerical example, we demonstrate that minimizing the derived bound on the convergence rate provides a practical approach to selecting algorithm parameters for particular ADMM instances. We complement our upper bound by constructing a nearly-matching lower bound on the worst-case rate of convergence.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Feb 2015.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 6; 2023: 1; 2024: 6; 2025: 4; 2026: 3.

22 papers.

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  1. 2022Robust and Explainable Autoencoders for Unsupervised Time Series Outlier Detection---Extended Versioncited by 19
  2. 2022A Reduction to Binary Approach for Debiasing Multiclass Datasetscited by 9
  3. 2022Convex Programs and Lyapunov Functions for Reinforcement Learning: A Unified Perspective on the Analysis of Value-Based Methodscited by 3
  4. 2022Solving Constrained Variational Inequalities via a First-order Interior Point-based Methodcited by 3
  5. 2024Primal Methods for Variational Inequality Problems with Functional Constraintscited by 3
  6. 2024Distributed Event-Based Learning via ADMMcited by 3
  7. 2021Distributed Sparse Feature Selection in Communication-Restricted Networkscited by 2
  8. 2024Semi-supervised Symmetric Non-negative Matrix Factorization with Low-Rank Tensor Representationcited by 2
  9. 2022SADAM: Stochastic Adam, A Stochastic Operator for First-Order Gradient-based Optimizercited by 1
  10. 2022DELMAR: Deep Linear Matrix Approximately Reconstruction to Extract Hierarchical Functional Connectivity in the Human Braincited by 1
  11. 2024Controlling Participation in Federated Learning with Feedbackcited by 1
  12. 2026LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimizationcited by 1
10 more
  1. 2021Generalized ADMM in Distributed Learning via Variational Inequalitycited by 0
  2. 2023Deep State-Space Model for Predicting Cryptocurrency Pricecited by 0
  3. 2024A General Continuous-Time Formulation of Stochastic ADMM and Its Variantscited by 0
  4. 2024Stability of Primal-Dual Gradient Flow Dynamics for Multi-Block Convex Optimization Problemscited by 0
  5. 2025Differentiable Projection-based Learn to Optimize in Wireless Network-Part I: Convex Constrained (Non-)Convex Programmingcited by 0
  6. 2025HOME-3: High-Order Momentum Estimator with Third-Power Gradient for Convex and Smooth Nonconvex Optimizationcited by 0
  7. 2025Permutation Randomization on Nonsmooth Nonconvex Optimization: A Theoretical and Experimental Studycited by 0
  8. 2025A Systems-Theoretic View on the Convergence of Algorithms under Disturbancescited by 0
  9. 2026Learning Over-Relaxation Policies for ADMM with Convergence Guaranteescited by 0
  10. 2026Co-VLA: Consensus-based Federated Training for Vision-Language-Action Modelscited by 0