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 Vol. 62; no. 10; pp. 4980 - 4993
Main Authors: Chenguang Xi, Khan, Usman A.
Format: Journal Article
Language:English
Published: IEEE 01.10.2017
Subjects:
Acceleration
Convergence
Directed graphs
Distributed algorithms
distributed optimization
Indexes
Linear programming
multiagent networks
Optimization
Symmetric matrices
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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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 <; τ <; 1, given that the objective functions are restricted strongly convex. The implementation of DEXTRA requires each agent to know its local out-degree. Simulation examples further illustrate our findings.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2672698