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

1 Citation (Scopus)

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

Fingerprint

Parallel algorithms
Directed graphs

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Liu, J., Fullmer, D., Nedich, A., Basar, T., & Morse, A. S. (2017). A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps. In 2017 American Control Conference, ACC 2017 (pp. 686-690). [7963032] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2017.7963032

A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps. / Liu, Ji; Fullmer, Daniel; Nedich, Angelia; Basar, Tamer; Morse, A. Stephen.

2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 686-690 7963032.

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

Liu, J, Fullmer, D, Nedich, A, Basar, T & Morse, AS 2017, A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps. in 2017 American Control Conference, ACC 2017., 7963032, Institute of Electrical and Electronics Engineers Inc., pp. 686-690, 2017 American Control Conference, ACC 2017, Seattle, United States, 5/24/17. https://doi.org/10.23919/ACC.2017.7963032
Liu J, Fullmer D, Nedich A, Basar T, Morse AS. A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps. In 2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 686-690. 7963032 https://doi.org/10.23919/ACC.2017.7963032
Liu, Ji ; Fullmer, Daniel ; Nedich, Angelia ; Basar, Tamer ; Morse, A. Stephen. / A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps. 2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 686-690
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