# Multi-Agent Distributed Optimization via Inexact Consensus ADMM

arXiv: https://arxiv.org/abs/1402.6065 · HTML: https://mlsanity.com/paper/1402.6065/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2014.

## Built on by (most cited first, 21 of 21)

- [Decentralized Riemannian Gradient Descent on the Stiefel Manifold](https://mlsanity.com/paper/2102.07091/) (2021)
- [FedADMM: A Robust Federated Deep Learning Framework with Adaptivity to System Heterogeneity](https://mlsanity.com/paper/2204.03529/) (2022)
- [Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function](https://mlsanity.com/paper/2112.14949/) (2021)
- [Distributed Learning With Sparsified Gradient Differences](https://mlsanity.com/paper/2202.02491/) (2022)
- [Federated Semi-Supervised Learning with Class Distribution Mismatch](https://mlsanity.com/paper/2111.00010/) (2021)
- [DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization](https://mlsanity.com/paper/2209.01850/) (2022)
- [Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning](https://mlsanity.com/paper/2203.02865/) (2022)
- [Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds](https://mlsanity.com/paper/2509.07779/) (2025)
- [A Variance-Reduced Stochastic Gradient Tracking Algorithm for Decentralized Optimization with Orthogonality Constraints](https://mlsanity.com/paper/2208.13643/) (2022)
- [Limited Communications Distributed Optimization via Deep Unfolded Distributed ADMM](https://mlsanity.com/paper/2309.14353/) (2023)
- [Decentralized Entropic Optimal Transport for Distributed Distribution Comparison](https://mlsanity.com/paper/2301.12065/) (2023)
- [Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality](https://mlsanity.com/paper/2401.09556/) (2024)
- [Distributed Policy Gradient for Linear Quadratic Networked Control with Limited Communication Range](https://mlsanity.com/paper/2403.03055/) (2024)
- [Distributed optimization: designed for federated learning](https://mlsanity.com/paper/2508.08606/) (2025)
- [Accelerating Distributed Optimization: A Primal-Dual Perspective on Local Steps](https://mlsanity.com/paper/2407.02689/) (2024)
- [A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraints](https://mlsanity.com/paper/2409.04998/) (2024)
- [Efficient Distributed Learning over Decentralized Networks with Convoluted Support Vector Machine](https://mlsanity.com/paper/2503.07563/) (2025)
- [CoCoL: A Communication Efficient Decentralized Collaborative Method for Multi-Robot Systems](https://mlsanity.com/paper/2508.20898/) (2025)
- [Pareto-optimal Trade-offs Between Communication and Computation with Flexible Gradient Tracking](https://mlsanity.com/paper/2509.18129/) (2025)
- [ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Design](https://mlsanity.com/paper/2510.16652/) (2025)
- [Distributed Quantum Gaussian Processes for Multi-Agent Systems](https://mlsanity.com/paper/2602.15006/) (2026)

## Abstract (arXiv)

Multi-agent distributed consensus optimization problems arise in many signal processing applications. Recently, the alternating direction method of multipliers (ADMM) has been used for solving this family of problems. ADMM based distributed optimization method is shown to have faster convergence rate compared with classic methods based on consensus subgradient, but can be computationally expensive, especially for problems with complicated structures or large dimensions. In this paper, we propose low-complexity algorithms that can reduce the overall computational cost of consensus ADMM by an order of magnitude for certain large-scale problems. Central to the proposed algorithms is the use of an inexact step for each ADMM update, which enables the agents to perform cheap computation at each iteration. Our convergence analyses show that the proposed methods converge well under some convexity assumptions. Numerical results show that the proposed algorithms offer considerably lower computational complexity than the standard ADMM based distributed optimization methods.