ADD-OPT: Accelerated Distributed Directed Optimization

In this paper, we consider distributed optimization problems where the goal is to minimize a sum of objective functions over a multiagent network. We focus on the case when the interagent communication is described by a strongly connected, directed graph. The proposed algorithm, Accelerated Distribu...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 63; no. 5; pp. 1329 - 1339
Main Authors Chenguang Xi, Ran Xin, Khan, Usman A.
Format Journal Article
LanguageEnglish
Published IEEE 01.05.2018
Subjects
Acceleration
Convergence
Convex functions
DEXTRA
directed graph
distributed optimization
Indexes
linear convergence
Linear programming
Optimization
Radio frequency
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Summary:In this paper, we consider distributed optimization problems where the goal is to minimize a sum of objective functions over a multiagent network. We focus on the case when the interagent communication is described by a strongly connected, directed graph. The proposed algorithm, Accelerated Distributed Directed OPTimization (ADDOPT), achieves the best known convergence rate for this class of problems, O(μ k ), 0 <; μ <; 1, given strongly convex, objective functions with globally Lipschitz-continuous gradients, where k is the number of iterations. Moreover, ADD-OPT supports a wider and more realistic range of step sizes in contrast to existing work. In particular, we show that ADD-OPT converges for arbitrarily small (positive) step sizes. Simulations further illustrate our results.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2737582