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

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 addin...

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Vydáno v:	Computational mathematics and mathematical physics Ročník 57; číslo 11; s. 1757 - 1770
Hlavní autoři:	Volkov, V. V., Erokhin, V. I., Krasnikov, A. S., Razumov, A. V., Khvostov, M. N.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Moscow Pleiades Publishing 01.11.2017 Springer Nature B.V
Témata:	Computational Mathematics and Numerical Analysis Linear programming Mathematics Mathematics and Statistics Matrix methods Simplex method Uniqueness improper linear programming problems minimal matrix correction dual pair of linear programming problems inverse linear programming problems Euclidean norm
ISSN:	0965-5425, 1555-6662
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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.
AbstractList	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.
Author	Volkov, V. V. Erokhin, V. I. Khvostov, M. N. Krasnikov, A. S. Razumov, A. V.
Author_xml	– sequence: 1 givenname: V. V. surname: Volkov fullname: Volkov, V. V. email: volkov@bsk.vsu.ru organization: Borisoglebsk Branch, Voronezh State University – sequence: 2 givenname: V. I. surname: Erokhin fullname: Erokhin, V. I. organization: Mozhaisky Military Space Academy – sequence: 3 givenname: A. S. surname: Krasnikov fullname: Krasnikov, A. S. organization: Russia State Social University – sequence: 4 givenname: A. V. surname: Razumov fullname: Razumov, A. V. organization: Mozhaisky Military Space Academy – sequence: 5 givenname: M. N. surname: Khvostov fullname: Khvostov, M. N. organization: Borisoglebsk Branch, Voronezh State University
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References_xml	– reference: EreminI. I.MazurovV. D.Astaf’evN. N.Improper Linear and Convex Programming Problems1983MoscowNauka0697.90061 – reference: GantmacherF. R.The Theory of Matrices1959New YorkChelsea0085.01001 – reference: Murav’evaO. V.Robustness and correction of linear modelsAutom. Remote Control2011723556569282844910.1134/S00051179110300761229.93044 – reference: Le DuyN.Decomposition method in correction problems for inconsistent systems of linear inequalities with partitioned matricesComput. Math. Math. Phys.2011511016851694290738110.1134/S0965542511100083 – reference: HornR. A.JohnsonC. R.Matrix Analysis1985CambridgeCambridge Univ. Press10.1017/CBO97805118108170576.15001 – reference: AmirkhanovaG. A.GolikovA. I.EvtushenkoYu. G.On an inverse linear programming problemProc. Steklov Inst. Math.201629512127346808410.1134/S008154381609003006727001 – reference: GorelikV. A.ErokhinV. 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Snippet	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...
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SubjectTerms	Computational Mathematics and Numerical Analysis Linear programming Mathematics Mathematics and Statistics Matrix methods Simplex method Uniqueness
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Title	Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems
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