# On the O(1/k) Convergence of Asynchronous Distributed Alternating Direction Method of Multipliers

arXiv: https://arxiv.org/abs/1307.8254 · HTML: https://mlsanity.com/paper/1307.8254/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2013.

## Built on by (most cited first, 11 of 11)

- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning](https://mlsanity.com/paper/2302.12559/) (2023)
- [Distributed Conformal Prediction via Message Passing](https://mlsanity.com/paper/2501.14544/) (2025)
- [Optimization in Open Networks via Dual Averaging](https://mlsanity.com/paper/2105.13348/) (2021)
- [Robust Online Learning over Networks](https://mlsanity.com/paper/2309.00520/) (2023)
- [Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approach](https://mlsanity.com/paper/2404.02511/) (2024)
- [A Class of Accelerated Fixed-Point-Based Methods with Delayed Inexact Oracles and Its Applications](https://mlsanity.com/paper/2512.13547/) (2025)
- [Pick your Neighbor: Local Gauss-Southwell Rule for Fast Asynchronous Decentralized Optimization](https://mlsanity.com/paper/2207.07543/) (2022)
- [Accelerating Distributed Optimization: A Primal-Dual Perspective on Local Steps](https://mlsanity.com/paper/2407.02689/) (2024)
- [Multi-Timescale Primal Dual Hybrid Gradient with Application to Distributed Optimization](https://mlsanity.com/paper/2506.15387/) (2025)
- [Fast and Efficient Asynchronous Gossip Algorithm for Robust and Non-Smooth Convex Decentralized Learning](https://mlsanity.com/paper/2601.20571/) (2026)

## Abstract (arXiv)

We consider a network of agents that are cooperatively solving a global optimization problem, where the objective function is the sum of privately known local objective functions of the agents and the decision variables are coupled via linear constraints. Recent literature focused on special cases of this formulation and studied their distributed solution through either subgradient based methods with O(1/sqrt(k)) rate of convergence (where k is the iteration number) or Alternating Direction Method of Multipliers (ADMM) based methods, which require a synchronous implementation and a globally known order on the agents. In this paper, we present a novel asynchronous ADMM based distributed method for the general formulation and show that it converges at the rate O(1/k).