Determination of Consistency and Inconsistency Radii for Systems of Linear Equations and Inequalities Using the Matrix l1 Norm

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 ra...

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Vydáno v:Computational mathematics and mathematical physics Ročník 58; číslo 6; s. 840 - 849
Hlavní autor: Murav’eva, O. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.06.2018
Témata:
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
matrix correction
inconsistent systems of linear equations and inequalities
consistency and inconsistency radii for systems of linear equations and inequalities
improper linear programming problems
ISSN:0965-5425, 1555-6662
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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.
AbstractList 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.
Author Murav’eva, O. V.
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Keywords matrix correction
inconsistent systems of linear equations and inequalities
consistency and inconsistency radii for systems of linear equations and inequalities
improper linear programming problems
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Title Determination of Consistency and Inconsistency Radii for Systems of Linear Equations and Inequalities Using the Matrix l1 Norm
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