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This paper proposes a novel family of primal-dual-based distributedalgorithms for smooth, convex, multi-agent optimization over networks that usesonly gradient information and gossip communications. The algorithms can alsoemploy acceleration on the computation and communications. We provide a unifiedanalysis of their convergence rate, measured in terms of the Bregman distanceassociated to the saddle point reformation of the distributed optimizationproblem. When acceleration is employed, the rate is shown to be optimal, in thesense that it matches (under the proposed metric) existing complexity lowerbounds of distributed algorithms applicable to such a class of problem andusing only gradient information and gossip communications. Preliminarynumerical results on distributed least-square regression problems show that theproposed algorithm compares favorably on existing distributed schemes.

Accelerated Primal-Dual Algorithms for Distributed Smooth Convex Optimization over Networks