LINEARLY CONVERGENT DECENTRALIZED CONSENSUS OPTIMIZATION OVER DIRECTED NETWORKS

Recently, there have been growing interests in solving distributed consensus optimization problems over directed networks that consist of multiple agents. In this paper, we develop a first-order (gradient-based) algorithm, referred to as Push-DIGing, for this class of problems. To run Push-DIGing, each agent in the network only needs to know its own out-degree and employs a fixed step-size. Under the strong convexity assumption, we prove that the introduced algorithm converges to the global minimizer at some R-linear (geometric) rate as long as the nonnegative step-size is no greater than some explicit bound.