Multi-Agent Distributed Optimization via Inexact Consensus ADMM

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 rat...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2015-01, Vol.63 (2), p.482-497
Main Authors: Chang, Tsung-Hui, Hong, Mingyi, Wang, Xiangfeng
Format: Article
Language:English
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
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2014.2367458