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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 11, Pages 1788–1803
DOI: https://doi.org/10.7868/S0044466917110151 (Mi zvmmf10635) 		 
This article is cited in 11 scientific papers (total in 11 papers)

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
Full-text PDF (300 kB) Citations (11)
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DOI: https://doi.org/10.7868/S0044466917110151
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.
Received: 24.10.2016
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 11, Pages 1757–1770
DOI: https://doi.org/10.1134/S0965542517110148
Bibliographic databases:
Document Type: Article
UDC: 519.612
Language: Russian
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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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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