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arXiv · 1611.06160

Linear convergence in optimization over directed graphs with row-stochastic matrices

Chenguang Xi·Van Sy Mai·Ran Xin·Eyad H. Abed·Usman A. Khan
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Abstract

This paper considers a distributed optimization problem over a multi-agent network, in which the objective function is a sum of individual cost functions at the agents. We focus on the case when communication between the agents is described by a \emph{directed} graph. Existing distributed optimization algorithms for directed graphs require at least the knowledge of the neighbors' out-degree at each agent (due to the requirement of column-stochastic matrices). In contrast, our algorithm requires no such knowledge. Moreover, the proposed algorithm achieves the best known rate of convergence for this class of problems, $O(μ^k)$ for $0<μ<1$, where $k$ is the number of iterations, given that the objective functions are strongly-convex and have Lipschitz-continuous gradients. Numerical experiments are also provided to illustrate the theoretical findings.

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Chenguang Xi, Van Sy Mai, Ran Xin, Eyad H. Abed, Usman A. Khan. 2017-10-30. Linear convergence in optimization over directed graphs with row-stochastic matrices. https://arxiv.org/abs/1611.06160

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