A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks

S. Sh Alaviani, Nicola Elia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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 languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages83-88
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Random Networks
Distributed Algorithms
Linear equations
Parallel algorithms
Algebraic Equation
Linear equation
Initial conditions
Graph in graph theory
Partitioned Matrix
Almost Sure Convergence
Convex optimization
Communication
Limit Point
Convex Optimization
Interconnection
Unique Solution
Iterative Algorithm
Connectivity
Optimization Problem
Converge

Cite this

Alaviani, S. S., & Elia, N. (2019). A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks. In 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.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 83-88 8618709 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Alaviani, SS & Elia, N 2019, A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks. in 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
Alaviani SS, Elia N. A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 83-88. 8618709. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8618709
Alaviani, S. Sh ; Elia, Nicola. / A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 83-88 (Proceedings of the IEEE Conference on Decision and Control).
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