Multi-Agent Distributed Optimization via Inexact Consensus ADMM

• Published in: IEEE transactions on signal processing Vol. 63; no. 2; pp. 482 - 497
• Main Authors: Chang, Tsung-Hui, Hong, Mingyi, Wang, Xiangfeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 15.01.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: ADMM; Algorithm design and analysis; Algorithms; Computation; Computational efficiency; consensus; Convergence; Cost function; Distributed databases; distributed optimization; Economic models; Mathematical models; Methods; Multiagent systems; Optimization; Optimization methods; Signal processing; Signal processing algorithms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2367458

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.