Distributed Stochastic Algorithm for Convex Optimization Over Directed Graphs

By introducing a surplus variable, a distributed stochastic algorithm is developed for convex optimization problem based on directed communication graphs. Firstly, in the proposed distributed algorithm, a surplus variable is introduced to overcome the unbalance graphs and relaxing the stringent double stochastic matrix condition. Besides, by formulating row stochastic matrix for decision variable and column stochastic matrix for surplus variable, we prove that the convergence rate of the proposed algorithm is O(lnk/k). Finally, for the purpose of showing the effectiveness of the proposed method, a numerical example are presented.