A Distributed Algorithm for Solving Linear Algebraic Equations over Random Networks

S. Sh Alaviani, N. Elia

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

6 Scopus citations

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

Bibliographical note

Funding Information:
This work was supported by National Science Foundation under Grant CCF-1320643, Grant CNS-1239319, and AFOSR Grant FA 9550-15-1- 0119..

Funding Information:
This work was supported by National Science Foundation under Grant CCF-1320643, Grant CNS-1239319, and AFOSR Grant FA 9550-15-1-0119.. The work has been done while N. Elia was at Iowa State University. The proofs and extensions of this paper appear in [44].

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