Geodesic
Correction of improper linear programming problems in canonical form by applying the minimax criterion
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2178-2189 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Correction of improper linear programming problems in canonical form by applying the minimax criterion},
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O. S. Barkalova. Correction of improper linear programming problems in canonical form by applying the minimax criterion. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2178-2189. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a5/

[1] Vatolin A. A., “Approksimatsiya nesobstvennykh zadach lineinogo programmirovaniya po kriteriyu evklidovoi normy”, Zh. vychisl. matem. i matem. fiz., 24:12 (1984), 1907–1908 | MR | Zbl

[2] Gorelik V. A., “Matrichnaya korrektsiya zadachi lineinogo programmirovaniya s nesovmestnoi sistemoi ogranichenii”, Zh. vychisl. matem. i matem. fiz., 41:11 (2001), 1697–1705 | MR | Zbl

[3] Gorelik V. A., Erokhin V. I., Pechenkin R. V., Chislennye metody korrektsii nesobstvennykh zadach lineinogo programmirovaniya i strukturnykh sistem uravnenii, VTs RAN, M., 2006 | MR

[4] Ibatullin R. R., Metody korrektsii i approksimatsii nesobstvennykh zadach optimizatsii i upravleniya s minimaksnym kriteriem, Diss. ... kand. fiz.-mat. nauk, M., 2002

[5] Voevodin V. V., Kuznetsov Yu. A., Teoriya matrits, Nauka, M., 1984 | MR | Zbl