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An Accelerated Linearized Alternating Direction Method of Multipliers

arXiv 1401.6607 ↗First posted 26 Jan 2014math.OCcited by 14

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Abstract (arXiv)

We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than that of linearized ADMM, in terms of their dependence on the Lipschitz constant of the smooth component. Moreover, AADMM is capable to deal with the situation when the feasible region is unbounded, as long as the corresponding saddle point problem has a solution. A backtracking algorithm is also proposed for practical performance.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Jan 2014.

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Citing papers per year: 2021: 2; 2022: 3; 2023: 3; 2024: 3; 2025: 3.

14 papers.

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  1. 2022Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimizationcited by 19
  2. 2023Complexity of Single Loop Algorithms for Nonlinear Programming with Stochastic Objective and Constraintscited by 16
  3. 2025Stochastic Smoothed Primal-Dual Algorithms for Nonconvex Optimization with Linear Inequality Constraintscited by 5
  4. 2024CRONOS: Enhancing Deep Learning with Scalable GPU Accelerated Convex Neural Networkscited by 4
  5. 2021A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimizationcited by 3
  6. 2021Transient growth of accelerated optimization algorithmscited by 2
  7. 2024Auto-conditioned primal-dual hybrid gradient method and alternating direction method of multiplierscited by 2
  8. 2022Tradeoffs between convergence rate and noise amplification for momentum-based accelerated optimization algorithmscited by 1
  9. 2023An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problemscited by 1
  10. 2023Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functionscited by 1
  11. 2025LAGO: Few-shot Crosslingual Embedding Inversion Attacks via Language Similarity-Aware Graph Optimizationcited by 1
  12. 2022Iterative Minimax Games with Coupled Linear Constraintscited by 0
2 more
  1. 2024A General Continuous-Time Formulation of Stochastic ADMM and Its Variantscited by 0
  2. 2025Simultaneous Learning and Optimization via Misspecified Saddle Point Problemscited by 0