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 - Publisher Copyright:
© 2017 American Automatic Control Council (AACC).
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
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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 -