Fast Consensus by the Alternating Direction Multipliers Method

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.