DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs

This paper develops a fast distributed algorithm, termed DEXTRA, to solve the optimization problem when n agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a directed graph. Exis...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2017-10, Vol.62 (10), p.4980-4993
Main Authors: Chenguang Xi, Khan, Usman A.
Format: Article
Language:English
Subjects:
Acceleration
Convergence
Directed graphs
Distributed algorithms
distributed optimization
Indexes
Linear programming
multiagent networks
Optimization
Symmetric matrices
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Summary:This paper develops a fast distributed algorithm, termed DEXTRA, to solve the optimization problem when n agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a directed graph. Existing algorithms solve the problem restricted to directed graphs with convergence √ rates of O(ln k/ √k) for general convex objective functions and O(ln k/k) when the objective functions are strongly convex, where k is the number of iterations. We show that, with the appropriate step-size, DEXTRA converges at a linear rate O(τ k ) for 0
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2672698