Decentralizing Consensus-Alternating Direction Method of Multipliers

Consensus-ADMM (C-ADMM) is devoid of being completely decentralized due to its dependency on star-topology and central coordinator. In this paper, we propose a novel algorithm for simultaneous optimization and consensus, to completely decentralize C-ADMM, and enabling implementation on any connected undirected graph. We present the necessary conditions on the algorithm parameters for it to be stable while proving its convergence. We also highlight the difference between our algorithm and Distributed-ADMM (D-ADMM), existing in literature. We show the way to choose algorithm parameters through simulations for desired results. We also show how our algorithm outperforms D-ADMM through simulations.