### Abstract

This paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers (ADMM). When rounding quantization is employed, a distributed ADMM algorithm is shown to converge to a consensus within 3 + log1+δ ω iterations where δ > 0 depends on the network topology and O is a polynomial of the quantization resolution, the agents' data and the network topology. A tight upper bound on the consensus error is also obtained, which depends only on the quantization resolution and the average degree of the graph. This bound is much preferred in large scale networks over existing algorithms whose consensus errors are increasing in the range of agents' data, the quantization resolution, and the number of agents. To minimize the consensus error, our final algorithm uses dithered quantization to obtain a good starting point and then adopts rounding quantization to reach a consensus. Simulations show that the consensus error of this algorithm is typically less than one quantization resolution for all connected networks with agents' data of arbitrary magnitudes.

Original language | English (US) |
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Title of host publication | 2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 692-696 |

Number of pages | 5 |

ISBN (Print) | 9781479975914 |

DOIs | |

State | Published - Feb 23 2016 |

Event | IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 - Orlando, United States Duration: Dec 13 2015 → Dec 16 2015 |

### Other

Other | IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 |
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Country | United States |

City | Orlando |

Period | 12/13/15 → 12/16/15 |

### Fingerprint

### Keywords

- alternating direction method of multipliers
- deterministic quantization
- Quantized consensus

### ASJC Scopus subject areas

- Information Systems
- Signal Processing

### Cite this

*2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015*(pp. 692-696). [7418285] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/GlobalSIP.2015.7418285

**Distributed average consensus with deterministic quantization : An ADMM approach.** / Zhu, Shengyu; Chen, Biao.

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

*2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015.*, 7418285, Institute of Electrical and Electronics Engineers Inc., pp. 692-696, IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015, Orlando, United States, 12/13/15. https://doi.org/10.1109/GlobalSIP.2015.7418285

}

TY - GEN

T1 - Distributed average consensus with deterministic quantization

T2 - An ADMM approach

AU - Zhu, Shengyu

AU - Chen, Biao

PY - 2016/2/23

Y1 - 2016/2/23

N2 - This paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers (ADMM). When rounding quantization is employed, a distributed ADMM algorithm is shown to converge to a consensus within 3 + log1+δ ω iterations where δ > 0 depends on the network topology and O is a polynomial of the quantization resolution, the agents' data and the network topology. A tight upper bound on the consensus error is also obtained, which depends only on the quantization resolution and the average degree of the graph. This bound is much preferred in large scale networks over existing algorithms whose consensus errors are increasing in the range of agents' data, the quantization resolution, and the number of agents. To minimize the consensus error, our final algorithm uses dithered quantization to obtain a good starting point and then adopts rounding quantization to reach a consensus. Simulations show that the consensus error of this algorithm is typically less than one quantization resolution for all connected networks with agents' data of arbitrary magnitudes.

AB - This paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers (ADMM). When rounding quantization is employed, a distributed ADMM algorithm is shown to converge to a consensus within 3 + log1+δ ω iterations where δ > 0 depends on the network topology and O is a polynomial of the quantization resolution, the agents' data and the network topology. A tight upper bound on the consensus error is also obtained, which depends only on the quantization resolution and the average degree of the graph. This bound is much preferred in large scale networks over existing algorithms whose consensus errors are increasing in the range of agents' data, the quantization resolution, and the number of agents. To minimize the consensus error, our final algorithm uses dithered quantization to obtain a good starting point and then adopts rounding quantization to reach a consensus. Simulations show that the consensus error of this algorithm is typically less than one quantization resolution for all connected networks with agents' data of arbitrary magnitudes.

KW - alternating direction method of multipliers

KW - deterministic quantization

KW - Quantized consensus

UR - http://www.scopus.com/inward/record.url?scp=84964758643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964758643&partnerID=8YFLogxK

U2 - 10.1109/GlobalSIP.2015.7418285

DO - 10.1109/GlobalSIP.2015.7418285

M3 - Conference contribution

SN - 9781479975914

SP - 692

EP - 696

BT - 2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -