A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps

Ji Liu, Daniel Fullmer, Angelia Nedich, Tamer Basar, A. Stephen Morse

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

This paper studies a distributed algorithm for finding a common fixed point of a family of m > 1 nonlinear maps Mi: Rn → Rn assuming that each map is strongly quasi-nonexpansive, and that at least one such common fixed point exists. A common fixed point is simultaneously and recursively computed by m agents assuming that each agent i knows only Mi, the current estimates of the fixed point generated by its neighbors, and nothing more. Neighbor relationships are described by a time-varying directed graph ℕ(t) whose vertices correspond to agents and whose arcs depict neighbor relationships. It is shown that for any sequence of repeatedly jointly strongly connected neighbor graphs ℕ(t), t ϵ {1, 2,⋯}, the algorithm causes all agents' estimates to converge to a common fixed point of Mi, i ϵ {1, 2,⋯, m}.

Original languageEnglish (US)
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages686-690
Number of pages5
ISBN (Electronic)9781509059928
DOIs
StatePublished - Jun 29 2017
Event2017 American Control Conference, ACC 2017 - Seattle, United States
Duration: May 24 2017May 26 2017

Other

Other2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period5/24/175/26/17

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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