An accelerated distributed optimization algorithm over time-varying digraphs with column-stochastic matrices

In this paper, the unconstrained distributed convex optimization problem over time-varying unbalanced directed graphs with column matrices is considered. To accelerate the existing distributed algorithm, a heavy-ball based convex optimization algorithm is proposed and its convergence proof is provided by the small gain theorem. Moreover, a nesterov acceleration method is added in the previous algorithm for further accelerating the convergence rate. Finally, some simulations are presented for illustrating the effectiveness.