Geodesic
Consistency and inconsistency radii for solving systems of linear equations and inequalities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 372-384 
O. V. Murav'eva. Consistency and inconsistency radii for solving systems of linear equations and inequalities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 372-384. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Problems that reduce to consistency or inconsistency of systems of linear equations or inequalities arise in many divisions of theoretical informatics. The examples are problems in linear programming, machine learning, multicriteria optimization, etc. There exist different stability measures for the property of consistency or inconsistency, and different information constituents are possible (all the input parameters, the coefficient matrix, the vector of constraints). In this paper, variations of all parameters are examined in combination with an additional constraint important in applications, namely, the nonnegativity of feasible points.

[1] Eremin I. I., “Obschaya teoriya ustoichivosti v lineinom programmirovanii”, Izv. Vuzov. Matem., 1999, no. 12, 43–52 | MR

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

[3] Muraveva O. V., “Robastnost i korrektsiya lineinykh modelei”, Avtomatika i telemekhan., 2011, no. 3, 98–112

[4] Eremin I. I., Mazurov V. D., Astafev N. N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983 | MR

[5] 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

[6] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR

[7] Muraveva O. V., “Vozmuschenie i korrektsiya sistem lineinykh neravenstv”, Upravlenie bolshimi sistemami, 28 (2010), 40–57