A Fast Algorithm for Distributed Optimization over Directed Networks

In this paper, we consider the distributed optimization problem over a directed network. In such practical network case, the double-stochasticity of mixing matrices and consensus may generally be violated. To deal with these challenges, we use non-doubly stochastic matrices and develop a new algorithm called ExtraPush via combining two well-known distributed algorithms, i.e., Extra and subgradient-push. The proposed algorithm uses a fixed step size like in Extra and accepts the column-stochastic mixing matrices like in subgradient-push. We present preliminary convergence analysis for ExtraPush under a bounded sequence assumption. Moreover, we provide a series of experiments to show the effectiveness, particularly, the fast convergence and consensus of the proposed algorithm.