### Abstract

This paper studies a distributed algorithm for finding a common fixed point of a family of m > 1 nonlinear maps M_{i}: R^{n} → R^{n} 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 M_{i}, 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 M_{i}, i ϵ {1, 2,⋯, m}.

Original language | English (US) |
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Title of host publication | 2017 American Control Conference, ACC 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 686-690 |

Number of pages | 5 |

ISBN (Electronic) | 9781509059928 |

DOIs | |

State | Published - Jun 29 2017 |

Event | 2017 American Control Conference, ACC 2017 - Seattle, United States Duration: May 24 2017 → May 26 2017 |

### Other

Other | 2017 American Control Conference, ACC 2017 |
---|---|

Country | United States |

City | Seattle |

Period | 5/24/17 → 5/26/17 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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 - Nedich, Angelia

AU - Basar, Tamer

AU - Morse, A. Stephen

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

SP - 686

EP - 690

BT - 2017 American Control Conference, ACC 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -