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In this paper, we introduce a fast row-stochastic decentralized algorithm,referred to as FRSD, to solve consensus optimization problems over directedcommunication graphs. The proposed algorithm only utilizes row-stochasticweights, leading to certain practical advantages in broadcast communicationsettings over those requiring column-stochastic weights. Under the assumptionthat each node-specific function is smooth and strongly convex, we show thatthe FRSD iterate sequence converges with a linear rate to the optimal consensussolution. In contrast to the existing methods for directed networks, FRSDenjoys linear convergence without employing a gradient tracking (GT) techniqueexplicitly, rather it implements GT implicitly with the use of a novel momentumterm, which leads to a significant reduction in communication and storageoverhead for each node when FRSD is implemented for solving high-dimensionalproblems over small-to-medium scale networks. In the numerical tests, wecompare FRSD with other state-of-the-art methods, which use row-stochasticand/or column-stochastic weights.

A Fast Row-Stochastic Decentralized Method for Distributed Optimization Over Directed Graphs