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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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542517110148