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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 3, Pages 53–63 (Mi da775)  

This article is cited in 1 scientific paper (total in 1 paper)

Stability of compatible systems of linear inequalities and linear separability

O. V. Muraveva

Moscow Pedagogical State University, 14 Krasnoprudnaya St., 107140 Moscow, Russia

Abstract: We consider methods of correction of matrices (or correction of all parameters) of systems of linear constraints (equations and inequalities). We show that the problem of matrix correction of an inconsistent system of linear inequalities with a non-negativity condition is reduced to a linear program. A stability measure of the feasible solution to a linear system is defined as the minimal possible variation of parameters at which this solution does not satisfy the system. The problem of finding the most stable solution to the system is considered. The results are applied to construct an optimal separating hyperplane that is the most stable to variations of the objects. Bibliogr. 15.

Keywords: stability of compatible system of linear inequalities, matrix correction, separating hyperplane.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:3, 349–356

Bibliographic databases:

UDC: 519.85
Received: 04.09.2013
Revised: 26.11.2013

Citation: O. V. Muraveva, “Stability of compatible systems of linear inequalities and linear separability”, Diskretn. Anal. Issled. Oper., 21:3 (2014), 53–63; J. Appl. Industr. Math., 8:3 (2014), 349–356

Citation in format AMSBIB
\Bibitem{Mur14}
\by O.~V.~Muraveva
\paper Stability of compatible systems of linear inequalities and linear separability
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 3
\pages 53--63
\mathnet{http://mi.mathnet.ru/da775}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242101}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 3
\pages 349--356
\crossref{https://doi.org/10.1134/S1990478914030065}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Volkov, V. I. Erokhin, A. S. Krasnikov, A. V. Razumov, M. N. Khvostov, “Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems”, Comput. Math. Math. Phys., 57:11 (2017), 1757–1770  mathnet  crossref  crossref  isi  elib
  • Дискретный анализ и исследование операций
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