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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 11, Pages 1788–1803 (Mi zvmmf10635)  

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

Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems

V. V. Volkova, V. I. Erokhinb, A. S. Krasnikovc, A. V. Razumovb, M. N. Khvostova

a Borisoglebsk Branch, Voronezh State University, Borisoglebsk, Voronezh oblast, Russia
b Mozhaisky Military Space Academy, St. Petersburg, Russia
c Russia State Social University, Moscow, Russia

Abstract: For a pair of dual (possibly improper) linear programming problems, a family of matrix corrections is studied that ensure the existence of given solutions to these problems. The case of correcting the coefficient matrix and three cases of correcting an augmented coefficient matrix (obtained by adding the right-hand side vector of the primal problem, the right-hand-side vector of the dual problem, or both vectors) are considered. Necessary and sufficient conditions for the existence of a solution to the indicated problems, its uniqueness is proved, and the form of matrices for the solution with a minimum Euclidean norm is presented. Numerical examples are given.

Key words: dual pair of linear programming problems, improper linear programming problems, inverse linear programming problems, minimal matrix correction, Euclidean norm.

DOI: https://doi.org/10.7868/S0044466917110151

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:11, 1757–1770

Bibliographic databases:

UDC: 519.612
Received: 24.10.2016

Citation: 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”, Zh. Vychisl. Mat. Mat. Fiz., 57:11 (2017), 1788–1803; Comput. Math. Math. Phys., 57:11 (2017), 1757–1770

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 11
\pages 1788--1803
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\pages 1757--1770
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    This publication is cited in the following articles:
    1. F. P. Vasil'ev, M. M. Potapov, L. A. Artem'eva, “Extragradient method for correction of inconsistent linear programming problems”, Comput. Math. Math. Phys., 58:12 (2018), 1919–1925  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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