Fast Consensus by the Alternating Direction Multipliers Method

• Published in: IEEE transactions on signal processing Vol. 59; no. 11; pp. 5523 - 5537
• Main Authors: Erseghe, T., Zennaro, D., Dall'Anese, E., Vangelista, L.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-11-2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Alternating direction multipliers method (ADMM); Applied sciences; Augmentation; Bismuth; Computer simulation; consensus; Convergence; convergence speed; Detection, estimation, filtering, equalization, prediction; distributed implementation; Eigenvalues and eigenfunctions; Exact sciences and technology; Indication; Information, signal and communications theory; Mathematical analysis; Multipliers; Nickel; Noise; noise resilience; Optimization; optimization methods; Quantization; Resilience; sensor networks; Signal and communications theory; Signal, noise; Telecommunications and information theory; Performance evaluation; Alternating direction method; Alternating direction multipliers method (ADMM); convergence speed; sensor networks; noise resilience; optimization methods; Distributed computing; Implementation; Optimization; Resilience; consensus; Algorithm performance; Simulation; distributed implementation; Convergence rate; Signal processing; Sensor array; Multiplying circuits; Signal detection
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2162831

The alternating direction multipliers method (ADMM) has been recently proposed as a practical and efficient algorithm for distributed computing. We discuss its applicability to the average consensus problem in this paper. By carefully relaxing ADMM augmentation coefficients we are able to analytically investigate its properties, and to propose simple and strict analytical bounds. These provide a clear indication on how to choose system parameters for optimized performance. We prove both analytically and via simulations that the proposed approach exhibits convergence speed between the best in the literature (classical and optimized solutions), while providing the most powerful resilience to noise.