{"url":"/method/admm","slug":"admm","name":"ADMM","full_name":"Alternating Direction Method of Multipliers","full_name_withheld":false,"description_markdown":"The **alternating direction method of multipliers** (**ADMM**) is an algorithm that solves convex optimization problems by breaking them into smaller pieces, each of which are then easier to handle. It takes the form of a decomposition-coordination procedure, in which the solutions to small\r\nlocal subproblems are coordinated to find a solution to a large global problem. ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. It turns out to be equivalent or closely related to many other algorithms\r\nas well, such as Douglas-Rachford splitting from numerical analysis, Spingarn’s method of partial inverses, Dykstra’s alternating projections method, Bregman iterative algorithms for l1 problems in signal processing, proximal methods, and many others.\r\n\r\nText Source: [https://stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf](https://stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf)\r\n\r\nImage Source: [here](https://www.slideshare.net/derekcypang/alternating-direction)","description_state":"present","introduced_year":null,"introduced_by":{"title":null,"paper":null,"first_author":null,"n_authors":0,"url_abs":null,"archive_paper_url":null},"source":{"url":null,"title":null,"url_on_a_paper_host":false},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"General","area_id":"general","collection":"Optimization","url":"/methods/category/optimization","pwc_aliases":[]}],"n_papers_tagged":398,"archive_num_papers":398,"papers_newest_first":[{"paper":"/paper/federated-admm-from-bayesian-duality","title":"Federated ADMM from Bayesian Duality","date":"2025-06-16","arxiv_id":"2506.13150","n_code_links":1,"syntology":{"ran":1,"of":2,"unverified":1,"pointer_only":2}},{"paper":null,"title":"Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming","date":"2025-06-02","arxiv_id":"2506.01826","n_code_links":0,"syntology":null},{"paper":"/paper/proximal-algorithm-unrolling-flexible-and","title":"Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging","date":"2025-05-29","arxiv_id":"2505.23180","n_code_links":1,"syntology":{"ran":6,"of":9,"unverified":3,"pointer_only":0}},{"paper":"/paper/linear-convergence-of-plug-and-play","title":"Linear Convergence of Plug-and-Play Algorithms with Kernel Denoisers","date":"2025-05-21","arxiv_id":"2505.15318","n_code_links":1,"syntology":null},{"paper":null,"title":"Optimization Problem Solving Can Transition to Evolutionary Agentic Workflows","date":"2025-05-07","arxiv_id":"2505.04354","n_code_links":0,"syntology":null},{"paper":null,"title":"Enhancing Variable Selection in Large-scale Logistic Regression: Leveraging Manual Labeling with Beneficial Noise","date":"2025-04-23","arxiv_id":"2504.16585","n_code_links":0,"syntology":null},{"paper":null,"title":"Residual-Evasive Attacks on ADMM in Distributed Optimization","date":"2025-04-22","arxiv_id":"2504.18570","n_code_links":0,"syntology":null},{"paper":null,"title":"Low-Complexity SDP-ADMM for Physical-Layer Multicasting in Massive MIMO Systems","date":"2025-04-08","arxiv_id":"2504.06090","n_code_links":0,"syntology":null},{"paper":null,"title":"Plug and Play Distributed Control of Clustered Energy Hub Networks","date":"2025-04-08","arxiv_id":"2504.06179","n_code_links":0,"syntology":null},{"paper":null,"title":"Distributed Mixed-Integer Quadratic Programming for Mixed-Traffic Intersection Control","date":"2025-04-06","arxiv_id":"2504.04618","n_code_links":0,"syntology":null},{"paper":"/paper/sparsity-promoting-reachability-analysis-and","title":"Sparsity-Promoting Reachability Analysis and Optimization of Constrained Zonotopes","date":"2025-04-04","arxiv_id":"2504.03885","n_code_links":1,"syntology":null},{"paper":null,"title":"Modular Distributed Nonconvex Learning with Error Feedback","date":"2025-03-18","arxiv_id":"2503.14055","n_code_links":0,"syntology":null},{"paper":null,"title":"Federated Smoothing ADMM for Localization","date":"2025-03-12","arxiv_id":"2503.09497","n_code_links":0,"syntology":null},{"paper":null,"title":"Efficient Distributed Learning over Decentralized Networks with Convoluted Support Vector Machine","date":"2025-03-10","arxiv_id":"2503.07563","n_code_links":0,"syntology":null},{"paper":null,"title":"An Adaptive Multiparameter Penalty Selection Method for Multiconstraint and Multiblock ADMM","date":"2025-02-28","arxiv_id":"2502.21202","n_code_links":0,"syntology":null},{"paper":null,"title":"Distributed Primal-Dual Algorithms: Unification, Connections, and Insights","date":"2025-02-01","arxiv_id":"2502.00470","n_code_links":0,"syntology":null},{"paper":null,"title":"Connecting Federated ADMM to Bayes","date":"2025-01-28","arxiv_id":"2501.17325","n_code_links":0,"syntology":null},{"paper":null,"title":"Three-Dimensional Diffusion-Weighted Multi-Slab MRI With Slice Profile Compensation Using Deep Energy Model","date":"2025-01-28","arxiv_id":"2501.17152","n_code_links":0,"syntology":null},{"paper":null,"title":"Asynchronous distributed collision avoidance with intention consensus for inland autonomous ships","date":"2025-01-27","arxiv_id":"2501.15899","n_code_links":0,"syntology":null},{"paper":"/paper/radio-map-estimation-via-latent-domain-plug","title":"Radio Map Estimation via Latent Domain Plug-and-Play Denoising","date":"2025-01-23","arxiv_id":"2501.13472","n_code_links":1,"syntology":null},{"paper":"/paper/a-plug-and-play-bregman-admm-module-for","title":"A Plug-and-Play Bregman ADMM Module for Inferring Event Branches in Temporal Point Processes","date":"2025-01-08","arxiv_id":"2501.04529","n_code_links":1,"syntology":null},{"paper":null,"title":"Constrained and Regularized Quantitative Ultrasound Parameter Estimation using ADMM","date":"2025-01-07","arxiv_id":"2501.04109","n_code_links":0,"syntology":null},{"paper":null,"title":"SLoG-Net: Algorithm Unrolling for Source Localization on Graphs","date":"2024-12-31","arxiv_id":"2501.00442","n_code_links":0,"syntology":null},{"paper":null,"title":"Iterative Reweighted Framework Based Algorithms for Sparse Linear Regression with Generalized Elastic Net Penalty","date":"2024-11-22","arxiv_id":"2411.14875","n_code_links":0,"syntology":null},{"paper":null,"title":"Decoupling Training-Free Guided Diffusion by ADMM","date":"2024-11-18","arxiv_id":"2411.12773","n_code_links":0,"syntology":null},{"paper":null,"title":"ADMM for Structured Fractional Minimization","date":"2024-11-12","arxiv_id":"2411.07496","n_code_links":0,"syntology":null},{"paper":"/paper/online-parallel-multi-task-relationship","title":"Online Parallel Multi-Task Relationship Learning via Alternating Direction Method of Multipliers","date":"2024-11-09","arxiv_id":"2411.06135","n_code_links":1,"syntology":null},{"paper":null,"title":"Deep Multi-contrast Cardiac MRI Reconstruction via vSHARP with Auxiliary Refinement Network","date":"2024-11-02","arxiv_id":"2411.01291","n_code_links":0,"syntology":null},{"paper":null,"title":"Distributed ADMM Approach for the Power Distribution Network Reconfiguration","date":"2024-10-06","arxiv_id":"2410.04604","n_code_links":0,"syntology":null},{"paper":null,"title":"An Analysis of Market-to-Market Coordination","date":"2024-10-02","arxiv_id":"2410.01986","n_code_links":0,"syntology":null}],"papers_shown":30,"tasks":[{"task":"/task/denoising","name":"Denoising","papers":30},{"task":"/task/distributed-optimization","name":"Distributed Optimization","papers":24},{"task":"/task/clustering","name":"Clustering","papers":18},{"task":"/task/machine-learning","name":"BIG-bench Machine Learning","papers":15},{"task":"/task/federated-learning","name":"Federated Learning","papers":15},{"task":"/task/image-reconstruction","name":"Image Reconstruction","papers":15},{"task":"/task/quantization","name":"Quantization","papers":15},{"task":"/task/image-restoration","name":"Image Restoration","papers":14},{"task":"/task/image-denoising","name":"Image Denoising","papers":13},{"task":"/task/regression-1","name":"regression","papers":13},{"task":"/task/computational-efficiency","name":"Computational Efficiency","papers":11},{"task":"/task/deep-learning","name":"Deep Learning","papers":11},{"task":"/task/model-compression","name":"Model Compression","papers":10},{"task":"/task/super-resolution","name":"Super-Resolution","papers":10},{"task":"/task/compressed-sensing","name":"compressed sensing","papers":10},{"task":"/task/deblurring","name":"Deblurring","papers":9},{"task":"/task/image-classification","name":"Image Classification","papers":9},{"task":"/task/privacy-preserving","name":"Privacy Preserving","papers":9},{"task":"/task/segmentation","name":"Segmentation","papers":8},{"task":"/task/semantic-segmentation","name":"Semantic Segmentation","papers":8}],"tasks_shown":20,"n_tasks":180,"usage_by_year":[{"year":"2013","papers":10},{"year":"2014","papers":12},{"year":"2015","papers":17},{"year":"2016","papers":22},{"year":"2017","papers":26},{"year":"2018","papers":28},{"year":"2019","papers":59},{"year":"2020","papers":43},{"year":"2021","papers":38},{"year":"2022","papers":41},{"year":"2023","papers":46},{"year":"2024","papers":34},{"year":"2025","papers":22}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/admm"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}