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 Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 6, Pages 873–882 (Mi zvmmf10700)

Determination of consistency and inconsistency radii for systems of linear equations and inequalities using the matrix $l_1$ norm

O. V. Murav'eva

Moscow Pedagogical State University, Moscow, Russia

Abstract: The problem of determining the minimal change in the coefficients of a consistent system of linear equations and inequalities that makes the system inconsistent is considered (the problem of determining the consistency radius of a system). If the original system is inconsistent, the inconsistency radius is defined as the solution to the problem of minimal correction of the coefficients upon which the system has a solution. For a homogeneous system of linear equations and inequalities, it is considered whether the property that a nonzero solution exists changes when correcting the parameters. A criterion for the correction magnitude is the sum of the moduli of all elements of the correction matrix. The problems of determining the consistency and inconsistency radii for systems of linear constraints written in different forms (with equality or inequality constraints and with the condition that some of the variables or all of them are nonnegative) reduce to a collection of finitely many linear programming problems.

Key words: matrix correction, inconsistent systems of linear equations and inequalities, consistency and inconsistency radii for systems of linear equations and inequalities, improper linear programming problems.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.8535.2017.

DOI: https://doi.org/10.7868/S0044466918060029

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:6, 840–849

Bibliographic databases:

UDC: 519.612
Revised: 20.07.2017

Citation: O. V. Murav'eva, “Determination of consistency and inconsistency radii for systems of linear equations and inequalities using the matrix $l_1$ norm”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 873–882; Comput. Math. Math. Phys., 58:6 (2018), 840–849

Citation in format AMSBIB
\Bibitem{Mur18} \by O.~V.~Murav'eva \paper Determination of consistency and inconsistency radii for systems of linear equations and inequalities using the matrix $l_1$ norm \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2018 \vol 58 \issue 6 \pages 873--882 \mathnet{http://mi.mathnet.ru/zvmmf10700} \crossref{https://doi.org/10.7868/S0044466918060029} \elib{https://elibrary.ru/item.asp?id=35096872} \transl \jour Comput. Math. Math. Phys. \yr 2018 \vol 58 \issue 6 \pages 840--849 \crossref{https://doi.org/10.1134/S0965542518060106} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438129700002} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049688525} 

• http://mi.mathnet.ru/eng/zvmmf10700
• http://mi.mathnet.ru/eng/zvmmf/v58/i6/p873

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. D. Skarin, “O vybore parametrov v metode kvazireshenii dlya korrektsii nesobstvennykh zadach vypuklogo programmirovaniya”, Tr. IMM UrO RAN, 26, no. 3, 2020, 187–197