TY - GEN

T1 - A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps

AU - Liu, Ji

AU - Fullmer, Daniel

AU - Nedic, Angelia

AU - Basar, Tamer

AU - Morse, A. Stephen

N1 - Funding Information:
The work of Liu and Basar was supported in part by AFOSR MURI Grant FA 9550-10-1-0573, and in part by Office of Naval Research (ONR) MURI Grant N00014-16-1-2710.
Publisher Copyright:
© 2017 American Automatic Control Council (AACC).
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/6/29

Y1 - 2017/6/29

N2 - 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}.

AB - 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}.

UR - http://www.scopus.com/inward/record.url?scp=85027021267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027021267&partnerID=8YFLogxK

U2 - 10.23919/ACC.2017.7963032

DO - 10.23919/ACC.2017.7963032

M3 - Conference contribution

AN - SCOPUS:85027021267

T3 - Proceedings of the American Control Conference

SP - 686

EP - 690

BT - 2017 American Control Conference, ACC 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 American Control Conference, ACC 2017

Y2 - 24 May 2017 through 26 May 2017

ER -