A Heavy-Ball Distributed Optimization Algorithm over Digraphs with Row-Stochastic Matrices

In this paper, we address the problem of distributed optimization in a multi-agent system, in which each agent maintains a private objective function and the goal of all agents is to cooperatively minimize the sum of their objects. By combining gradient-tracking method and heavy-ball method, a novel accelerated distributed optimization algorithm is proposed under the scenario that the underlying communication network is general directed with row-stochastic weighted matrix, which is easier to be realized in practice than the case of column-stochastic weighted matrix. It is proved that the algorithm converges at a geometric rate as long as the step-size α and the momentum coefficient β do not exceed certain bounds. Finally, numerical experiments are performed to illustrate the performance of our algorithm.