### Abstract

In this paper, the problem of solving linear algebraic equations of the form Ax=b among multi agents is considered. It is assumed that the interconnection graphs over which the agents communicate are random. It is assumed that each agent only knows a subset of rows of the partitioned matrix [A, b]. The problem is formulated such that this formulation does not require distribution dependency of random communication graphs. The random Krasnoselskii-Mann iterative algorithm is applied for almost sure convergence to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm converges almost surely independently from the distribution and, therefore, is amenable to completely asynchronous operations withot B-connectivity assumption. Based on initial conditions of agents' states, we show that the limit point of the sequence generated by the algorithm is determined by the unique solution of a convex optimization problem independent from the distribution of random communication graphs.

Original language | English (US) |
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Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 83-88 |

Number of pages | 6 |

ISBN (Electronic) | 9781538613955 |

DOIs | |

State | Published - Jan 18 2019 |

Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 2018-December |

ISSN (Print) | 0743-1546 |

### Conference

Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
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Country | United States |

City | Miami |

Period | 12/17/18 → 12/19/18 |

### Fingerprint

### Cite this

*2018 IEEE Conference on Decision and Control, CDC 2018*(pp. 83-88). [8618709] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8618709

**A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks.** / Alaviani, S. Sh; Elia, Nicola.

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

*2018 IEEE Conference on Decision and Control, CDC 2018.*, 8618709, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 83-88, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8618709

}

TY - GEN

T1 - A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks

AU - Alaviani, S. Sh

AU - Elia, Nicola

PY - 2019/1/18

Y1 - 2019/1/18

N2 - In this paper, the problem of solving linear algebraic equations of the form Ax=b among multi agents is considered. It is assumed that the interconnection graphs over which the agents communicate are random. It is assumed that each agent only knows a subset of rows of the partitioned matrix [A, b]. The problem is formulated such that this formulation does not require distribution dependency of random communication graphs. The random Krasnoselskii-Mann iterative algorithm is applied for almost sure convergence to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm converges almost surely independently from the distribution and, therefore, is amenable to completely asynchronous operations withot B-connectivity assumption. Based on initial conditions of agents' states, we show that the limit point of the sequence generated by the algorithm is determined by the unique solution of a convex optimization problem independent from the distribution of random communication graphs.

AB - In this paper, the problem of solving linear algebraic equations of the form Ax=b among multi agents is considered. It is assumed that the interconnection graphs over which the agents communicate are random. It is assumed that each agent only knows a subset of rows of the partitioned matrix [A, b]. The problem is formulated such that this formulation does not require distribution dependency of random communication graphs. The random Krasnoselskii-Mann iterative algorithm is applied for almost sure convergence to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm converges almost surely independently from the distribution and, therefore, is amenable to completely asynchronous operations withot B-connectivity assumption. Based on initial conditions of agents' states, we show that the limit point of the sequence generated by the algorithm is determined by the unique solution of a convex optimization problem independent from the distribution of random communication graphs.

UR - http://www.scopus.com/inward/record.url?scp=85062177790&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062177790&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8618709

DO - 10.1109/CDC.2018.8618709

M3 - Conference contribution

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 83

EP - 88

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -