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Studying the stability of solutions to systems of linear inequalities and constructing separating hyperplanes

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Abstract

We consider the methods for matrix correction or correction of all parameters of systems of linear equations and inequalities. We show that the problem of matrix correction of an inconsistent system of linear inequalities with the nonnegativity condition is reduced to a linear programming problem. Some stability measure is defined for a given solution to a system of linear inequalities as the minimal possible variation of parameters under 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 constructing an optimal separating hyperplane in the feature space that is the most stable to the changes of features of the objects.

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Authors and Affiliations

  1. Moscow Pedagogical State University, ul. Krasnoprudnaya 14, Moscow, 107140, Russia

    O. V. Murav’eva

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  1. O. V. Murav’eva
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Correspondence to O. V. Murav’eva.

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Original Russian Text © O.V. Murav’eva, 2014, published in Diskretnyi Analiz i Issledovanie Operatsii, 2014, Vol. 21, No. 3, pp. 53–63.

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Murav’eva, O.V. Studying the stability of solutions to systems of linear inequalities and constructing separating hyperplanes. J. Appl. Ind. Math. 8, 349–356 (2014). https://doi.org/10.1134/S1990478914030065

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  • DOI: https://doi.org/10.1134/S1990478914030065

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