Linear Convergence in Optimization Over Directed Graphs With Row-Stochastic Matrices
This paper considers a distributed optimization problem over a multiagent 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 directed graph. Existing distributed optimization algor...
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Published in | IEEE transactions on automatic control Vol. 63; no. 10; pp. 3558 - 3565 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
New York
IEEE
01.10.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subjects | |
Online Access | Get full text |
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Summary: | This paper considers a distributed optimization problem over a multiagent 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 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, <inline-formula><tex-math notation="LaTeX"> O(\mu ^k)</tex-math></inline-formula> for <inline-formula><tex-math notation="LaTeX">0<\mu <1</tex-math> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> 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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ISSN: | 0018-9286 1558-2523 |
DOI: | 10.1109/TAC.2018.2797164 |