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dc.contributor.authorLi, Xiuxianen_US
dc.contributor.authorXie, Lihuaen_US
dc.identifier.citationLi, X. & Xie, L. (2020). Distributed algorithms for computing a fixed point of multi-agent nonexpansive operators. Automatica, 122, 109286-.
dc.description.abstractThis 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.en_US
dc.description.sponsorshipMinistry of Education (MOE)en_US
dc.rights© 2020 Elsevier Ltd. All rights reserved.en_US
dc.subjectEngineering::Electrical and electronic engineeringen_US
dc.titleDistributed algorithms for computing a fixed point of multi-agent nonexpansive operatorsen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Electrical and Electronic Engineeringen_US
dc.subject.keywordsDistributed Algorithmsen_US
dc.subject.keywordsMulti-agent Networksen_US
dc.description.acknowledgementThis work was supported by the Ministry of Education of Singapore under MoE Tier 1 Research Grant RG72.en_US
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