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
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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