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Title: Distributed algorithms for computing a fixed point of multi-agent nonexpansive operators
Authors: Li, Xiuxian
Xie, Lihua
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2020
Source: Li, X. & Xie, L. (2020). Distributed algorithms for computing a fixed point of multi-agent nonexpansive operators. Automatica, 122, 109286-.
Project: RG72
Journal: Automatica
Abstract: This paper investigates the problem of finding a fixed point for a global nonexpansive operator under time-varying communication graphs in real Hilbert spaces, where the global operator is separable and composed of an aggregate sum of local nonexpansive operators. Each local operator is only privately accessible to each agent, and all agents constitute a network. To seek a fixed point of the global operator, it is indispensable for agents to exchange local information and update their solution cooperatively. To solve the problem, two algorithms are developed, called distributed Krasnosel'skiĭ–Mann (D-KM) and distributed block-coordinate Krasnosel'skiĭ–Mann (D-BKM) iterations, for which D-BKM is a block-coordinate version of D-KM in the sense of randomly choosing and computing only one block-coordinate of local operators at each time for each agent. It is shown that the proposed two algorithms can both converge weakly to a fixed point of the global operator. Meanwhile, the designed algorithms are applied to recover the classical distributed gradient descent (DGD) algorithm, devise a new block-coordinate DGD algorithm, handle a distributed shortest distance problem in the Hilbert space for the first time, and solve linear algebraic equations in a novel distributed approach. Finally, the theoretical results are corroborated by a few numerical examples.
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2020.109286
Rights: © 2020 Elsevier Ltd. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:EEE Journal Articles

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