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Gradient-push algorithm has been widely used for decentralized optimizationproblems when the connectivity network is a direct graph. This paper shows thatthe gradient-push algorithm with stepsize $\alpha>0$ converges exponentiallyfast to an $O(\alpha)$-neighborhood of the optimizer under the assumption thateach cost is smooth and the total cost is strongly convex. Numericalexperiments are provided to support the theoretical convergence results.

On the convergence result of the gradient-push algorithm on directed graphs with constant stepsize