## Abstract

In this paper, we consider the unconstrained distributed optimization problem, in which the exchange of information in the network is captured by a directed graph topology, thus, nodes can only communicate with their neighbors. Additionally, in our problem, the communication channels among the nodes have limited bandwidth. In order to alleviate this limitation, quantized messages should be exchanged among the nodes. For solving this distributed optimization problem, we combine a gradient descent method with a distributed quantized consensus algorithm (which requires the nodes to exchange quantized messages and converges in a finite number of steps). Specifically, at every optimization step, each node (i) performs a gradient descent step (i.e., subtracts the scaled gradient from its current estimate), and (ii) performs a finite-time calculation of the quantized average of every node's estimate in the network. As a consequence, this algorithm approximately mimics the centralized gradient descent algorithm. We show that our algorithm asymptotically converges to a neighborhood of the optimal solution with linear convergence rate. The performance of the proposed algorithm is demonstrated via simple illustrative examples.

Original language | English |
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Title of host publication | IFAC-PapersOnLine |

Editors | Hideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita |

Publisher | Elsevier |

Pages | 5900-5906 |

Number of pages | 7 |

Edition | 2 |

ISBN (Electronic) | 978-1-7138-7234-4 |

DOIs | |

Publication status | Published - 1 Jul 2023 |

MoE publication type | A4 Conference publication |

Event | IFAC World Congress - Yokohama, Japan Duration: 9 Jul 2023 → 14 Jul 2023 Conference number: 22 |

### Publication series

Name | IFAC-PapersOnLine |
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Number | 2 |

Volume | 56 |

ISSN (Electronic) | 2405-8963 |

### Conference

Conference | IFAC World Congress |
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Country/Territory | Japan |

City | Yokohama |

Period | 09/07/2023 → 14/07/2023 |

## Keywords

- directed graphs
- Distributed optimization
- finite-time consensus
- quantized communication