Distributed ADMM over directed networks.

Abstract

Distributed optimization over a network of agents is ubiquitous with applications in areas including power system control, robotics and statistical learning. In many settings, the communication network is directed, i.e., the communication links between agents are unidirectional. While several variations of gradient-descent-based primal methods have been proposed for distributed optimization over directed networks, an extension of dual-ascent methods to directed networks remains a less-explored area. In this paper, we propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) for directed networks. ADMM is a dual-ascent method that is known to perform well in practice. We show that if the objective function is smooth and strongly convex, our distributed ADMM algorithm achieves a geometric rate of convergence to the optimal point. Through numerical examples, we observe that the performance of our algorithm is comparable with some state-of-the-art distributed optimization algorithms over directed graphs. Additionally, our algorithm is observed to be robust to changes in its parameters.