Alternating Direction Method of Multipliers

Also known as ADMM

ADMM studies how to solve constrained optimization problems by splitting them into simpler subproblems and coordinating their solutions with dual-variable updates. Consensus, proximal, linearized, and multi-block variants are used in distributed learning, inverse problems, model-predictive control, robotics, and compression; common evaluations include image reconstruction, quadratic-program benchmarks, and trajectory-planning tasks. Current work combines ADMM with GPU implementations, learned parameter updates, and deep unfolding, while plug-and-play variants incorporate denoisers or generative priors. A central tension is how to gain speed and flexibility without losing convergence and constraint guarantees, particularly for nonconvex or multi-block problems where convergence can fail.

Latest papers

32 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

A Multi-Step Inertial ADMM Algorithm for Federated Learning
Oct 17, 2026Hao Li, Qingsong Wang, Xihong Yan +2Federated Learning Alternating Direction Method of Multipliers
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China · Shanxi Key Laboratory for Intelligent Optimization Computing and Block-chain Technology, School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, China · School of Mathematical Sciences, Beihang University, Beijing 100191, China
Markovian Nonconvex ADMM for Reinforcement Learning: Bellman-Resolvent Stability Beyond Smooth Blocks
Sep 29, 2026Zhaojun PengAlternating Direction Method of Multipliers RL Control
SPADE-DFL: Communication-Efficient Decentralized Federated Learning via Derivative-Free Linearized ADMM
Sep 24, 2026Mengli Wei, Mengkai Zhu, Jiawen Chen +2Communication-Efficient Distributed Training Black-Box Optimization
School of Mathematics, Southeast University, Nanjing 210096, China
Contact-Implicit Stein Projected ADMM for Discovery of Diverse Contact-Rich Manipulation Strategies
Sep 23, 2026Hrishikesh Sathyanarayan, Christian Hughes, Ian AbrahamContact-Rich Robotic Manipulation Trajectory Optimization
Department of Mechanical Engineering, Yale University, New Haven, CT, USA. · Department of Electrical Engineering, University of Sydney, NSW, Australia.
AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block
Aug 14, 2026Kenan Xu, Xiangfeng WangAI-Assisted Mathematical Discovery Alternating Direction Method of Multipliers
School of Mathematical Sciences, East China Normal University, Shanghai 200241, P.R. China. · Key Laboratory of Mathematics and Engineering Applications (MoE) and School of Mathematical Sciences, East China Normal University, Shanghai 200241, P.R. China.
Learning-enabled Acceleration of Scenario-based Model Predictive Control
Jul 14, 2026Trinh Tran, Binh Nguyen, Truong X. NghiemAlternating Direction Method of Multipliers Model Predictive Control
Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA
WarpMPC: Large-Batch MPC on GPU via ADMM with Unrolled $LDL^\top$ Factorization
Jul 13, 2026Henrik Hose, Se Hwan Jeon, Charles Khazoom +2GPU Kernel Optimization GPU Acceleration
Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University, Germany · Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA, USA.
Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization
Jun 26, 2026Shuang Li, Zhihui Zhu, Qiuwei LiOptimization Convergence Analysis Distributed Optimization
Department of Electrical and Computer Engineering, Iowa State University, Ames, Iowa 50014, USA · Department of Computer Science and Engineering, Ohio State University, Columbus, Ohio 43210, USA · DAMO Academy, Alibaba Group US, Bellevue, Washington 98004, USA
Deep-Unfolded Coordination
Jun 18, 2026Hunter Kuperman, Minchan Jung, Rahul V. Ghosh +2Trajectory Optimization Multi-Agent System Optimization
Autonomous Control and Decision Systems Laboratory Georgia Institute of Technology United States
LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization
Jun 8, 2026Binh Nguyen, Trinh Tran, Truong X. NghiemLearning to Optimize Alternating Direction Method of Multipliers
Department of Electrical and Computer Engineering, College of Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA
Physics-Aware Linearized ADMM and Its Unrolling
Jun 1, 2026Satoshi Takabe, Shunta Arai, Tadashi WadayamaAlternating Direction Method of Multipliers Algorithm Unrolling
Department of Computer Science Institute of Science Tokyo Tokyo, Japan · Center for Advanced Intelligence Project RIKEN Tokyo, Japan · Department of Engineering Nagoya Institute of Technology Nagoya, Japan
Learning Multi-Agent Coordination via Sheaf-ADMM
May 29, 2026Jeffrey Seely, Bartłomiej Cupiał, Llion JonesMulti-Agent System Optimization Multi-Agent Coordination
Sakana AI, Tokyo, Japan · University of Warsaw · AKCES NCBR
A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learning
May 19, 2026Honglin Du, Muxuan Liang, Xiang ZhongStructural Causal Models Clustering
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA · Department of Biostatistics, MD Anderson Cancer Center, Houston, TX 77030, USA
ADMM-Q: An Improved Hessian-based Weight Quantizer for Post-Training Quantization of Large Language Models
May 11, 2026Ryan Lucas, Mehdi Makni, Xiang Meng +2LLM Quantization Alternating Direction Method of Multipliers
MIT Operations Research Center · MIT Sloan School of Management · MIT Center for Statistics
Function-Space ADMM for Decentralized Federated Learning: A Control Theoretic Perspective
May 10, 2026Akihito Taya, Yuuki Nishiyama, Kaoru SezakiAlternating Direction Method of Multipliers Non-IID Federated Learning
Institute of Industrial Science, The University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan · Center for Spatial Information Science, The University of Tokyo, Kashiwa-shi, Chiba 277-8568, Japan
FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors
May 9, 2026Hendrik Sommerhoff, Michael MoellerAlternating Direction Method of Multipliers Image Restoration
Computer Vision Group, University of Siegen Hölderlinstraße 3, 57076 Siegen, Germany
Low Rank Tensor Completion via Adaptive ADMM
May 5, 2026Niclas Führling, Getuar Rexhepi, Giuseppe Thadeu Freitas de AbreuTensor Completion Nuclear Norm Minimization
School of Computer Science and Engineering, Constructor University, Bremen, Germany
Learning Over-Relaxation Policies for ADMM with Convergence Guarantees
Apr 29, 2026Junan Lin, Paul J. Goulart, Luca FurieriLearning to Optimize Alternating Direction Method of Multipliers
Department of Engineering Science, University of Oxford, OX1 3PJ Oxford, UK
ATRS: Adaptive Trajectory Re-splitting via a Shared Neural Policy for Parallel Optimization
Apr 24, 2026Jiajun Yu, Guodong Liu, Li Wang +6Trajectory Optimization Alternating Direction Method of Multipliers
HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization
Apr 14, 2026Trinh Tran, Binh Nguyen, Truong X. NghiemLearning to Optimize Alternating Direction Method of Multipliers
Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA
Machine Learning-Assisted High-Dimensional Matrix Estimation
Mar 30, 2026Wan Tian, Hui Yang, Zhouhui Lian +2Learning to Optimize Alternating Direction Method of Multipliers
Advanced Institute of Information Technology, Peking University · Wangxuan Institute of Computer Technology, Peking University, China, 100871 · Guanghua School of Management, Peking University, Beijing, China, 100871 +3
Collision-Free Velocity Scheduling for Multi-Agent Systems on Predefined Routes via Inexact-Projection ADMM
Mar 23, 2026Seungyeop Lee, Jong-Han KimMulti-Agent Coordination Collision Avoidance
Department of Aerospace Engineering and the Program in Aerospace Systems Convergence, Inha University, Incheon, South Korea. · Aerospace Systems Research Institute, Inha University, Incheon, South Korea.
ADMM-based Continuous Trajectory Optimization in Graphs of Convex Sets
Mar 11, 2026Lukas Pries, Jon Arrizabalaga, Zachary Manchester +1Trajectory Optimization Alternating Direction Method of Multipliers
Autonomous Aerial Systems Lab, Dep. of Aerospace and Geodesy, TU Munich, Germany · Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, USA
Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework
Mar 10, 2026Rajesh Shrestha, Xiao FuDiffusion-Based Inverse Problems Inverse Problems
School of EECS, Oregon State University
cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization
Mar 3, 2026Jiawei Wang, Arshiya Taj Abdul, Evangelos A. TheodorouSecond-Order Cone Programming Trajectory Optimization
University of California, San Diego · Georgia Institute of Technology, Atlanta
3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs
Mar 2, 2026Mehdi Makni, Xiang Meng, Rahul MazumderLLM Compression Low-Rank Compression
Operations Research Center Massachusetts Institute of Technology
riMESA: Consensus ADMM for Real-World Collaborative SLAM
Mar 1, 2026Daniel McGann, Michael KaessSimultaneous Localization and Mapping Pose Graph Optimization
The authors are with the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA.
Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction
Feb 26, 2026Chenhe Du, Xuanyu Tian, Qing Wu +4Image Reconstruction Diffusion-Based Inverse Problems
ShanghaiTech University · Shanghai Jiao Tong University
Hybrid System Planning using a Mixed-Integer ADMM Heuristic and Hybrid Zonotopes
Feb 19, 2026Joshua A. Robbins, Andrew F. Thompson, Jonah J. Glunt +1Motion Planning Alternating Direction Method of Multipliers
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802 USA
Learning to Optimize by Differentiable Programming
Jan 23, 2026Liping Tao, Xindi Tong, Chee Wei TanPrimal-Dual Optimization Learning to Optimize
Nanyang Technological University, Singapore · Nanyang Technological University, Singapore, Singapore

Oct 17, 2026J/K move · Enter open · S save

A Multi-Step Inertial ADMM Algorithm for Federated Learning

Hao Li, Qingsong Wang, Xihong Yan, Chengcheng Yan+1

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China · Shanxi Key Laboratory for Intelligent Optimization Computing and Block-chain Technology, School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, China · School of Mathematical Sciences, Beihang University, Beijing 100191, China

Federated Learning Alternating Direction Method of Multipliers

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Federated learning has recently emerged as an important paradigm for large-scale distributed model training, which can be naturally formulated as a class of distributed learning problems. The alternating direction method of multipliers (ADMM) is a widely used approach for solving such problems. However, its practical performance is often hindered by significant communication overhead and system heterogeneity. In this paper, we propose a multi-step inertial ADMM algorithm, called MiFedADMM, for federated learning. The proposed method leverages multiple historical iterates on the server side to construct a higher-order extrapolation after each aggregation to accelerate the convergence behavior. Under mild assumptions, we establish convergence results for the single-step variant of the proposed method and derive an O(1/K) convergence rate. Numerical experiments on both synthetic and real-world datasets demonstrate the effectiveness and improved performance of the proposed method compared with existing approaches.