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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Bibliographic Details
Published in:	Computational mathematics and mathematical physics Vol. 57; no. 11; pp. 1757 - 1770
Main Authors:	Volkov, V. V., Erokhin, V. I., Krasnikov, A. S., Razumov, A. V., Khvostov, M. N.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01.11.2017 Springer Nature B.V
Subjects:	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
Online Access:	Get full text
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Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0965-5425 1555-6662
DOI:	10.1134/S0965542517110148