Correction of improper linear programming problems in canonical form by applying the minimax criterion

Given an inconsistent system of linear algebraic equations, necessary and sufficient conditions are established for the solvability of the problem of its matrix correction by applying the minimax criterion with the assumption that the solution is nonnegative. The form of the solution to the correcte...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 52; no. 12; pp. 1624 - 1634
Main Author: Barkalova, O. S.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.12.2012
Springer Nature B.V
Subjects:
Algebra
Computational mathematics
Computational Mathematics and Numerical Analysis
Criteria
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Matlab
Matrix
Minimax technique
Simplex method
Studies
Vectors (mathematics)
matrix correction
inconsistent system of linear algebraic equations
minimax criterion
improper linear programming problem
MATLAB
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:Given an inconsistent system of linear algebraic equations, necessary and sufficient conditions are established for the solvability of the problem of its matrix correction by applying the minimax criterion with the assumption that the solution is nonnegative. The form of the solution to the corrected system is presented. Two formulations of the problem are considered, specifically, the correction of both sides of the original system and correction with the right-hand-side vector being fixed. The minimax-criterion correction of an improper linear programming problem is reduced to a linear programming problem, which is solved numerically in MATLAB.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542512120044