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 inIEEE transactions on automatic control Vol. 62; no. 10; pp. 4980 - 4993
Main Authors Chenguang Xi, Khan, Usman A.
Format Journal Article
LanguageEnglish
Published IEEE 01.10.2017
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 <; 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