Distributed ADMM with linear updates over directed networks

In this paper, we propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) with linear updates for directed networks. We show that if the objective function of the minimization problem is smooth and strongly convex, our distributed ADMM algorithm achieves a geometric rate of convergence to the optimal point. Through numerical examples, we demonstrate that our algorithm gives a performance that is comparable with that of state-of-the-art ADMM methods over directed graphs, while it outperforms these methods on special kinds of graphs with large diameters. Additionally, our algorithm is observed to be robust to changes in its parameters