On some sufficient conditions for the solvability and unsolvability of matrix correction problems for improper linear programming problems

V. I. Erokhin

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 110-116

Résumé

Sufficient solvability conditions and sufficient unsolvability conditions are given for matrix correction problems related to a pair of mutually dual improper linear programming problems with respect to the minimum of the matrix Euclidean norm in the case when no additional constraints are imposed on the correction matrix.

Détail

Keywords: improper linear programming
Mots-clés : matrix correction.

Bibliographie

[1] Astafev N.N., “Dvoistvennye sistemy odnorodnykh lineinykh uravnenii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19:2 (2013), 48–53 | MR

[2] Ashmanov S.A., Timokhov A.V., Teoriya optimizatsii v zadachakh i uprazhneniyakh, Nauka, M., 1991, 448 pp.

[3] Vasilev F.P., Ivanitskii A.Yu., Lineinoe programmirovanie, Faktorial Press, M., 2008, 328 pp. | MR

[4] Vatolin A.A., “Approksimatsiya nesobstvennykh zadach lineinogo programmirovaniya po kriteriyu evklidovoi normy”, Zhurn. vychisl. matematiki i mat. fiziki, 24:12 (1984), 1907–1908 | MR | Zbl

[5] Golikov A.I., Evtushenko Yu.G., “Primenenie teorem ob alternativakh k nakhozhdeniyu normalnykh reshenii lineinykh sistem”, Izv. vuzov. Matematika, 2001, no. 12(475), 21–31 | MR | Zbl

[6] Golikov A.I., Evtushenko Yu.G., “Teoremy ob alternativakh i ikh primenenie v chislennykh metodakh”, Zhurn. vychisl. matematiki i mat. fiziki, 43:3 (2003), 354–375 | MR | Zbl

[7] Golikov A.I., Evtushenko Yu.G., “Regulyarizatsiya i normalnye resheniya sistem lineinykh uravnenii i neravenstv”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:2 (2014), 113–121 | MR

[8] Gorelik V.A., Kondrateva V.A., “Parametricheskoe programmirovanie i nesobstvennye zadachi lineinoi optimizatsii”, Modelirovanie, optimizatsiya i dekompozitsiya slozhnykh dinamicheskikh protsessov, VTs RAN, M., 1999, 57–82 | MR

[9] Gorelik V.A., Erokhin V.I., Muraveva O.V., “Nekotorye zadachi approksimatsii matrits koeffitsientov nesovmestnykh sistem lineinykh uravnenii i nesobstvennykh zadach lineinogo programmirovaniya”, Modelirovanie, optimizatsiya i dekompozitsiya slozhnykh dinamicheskikh protsessov, VTs RAN, M., 2001, 57–88 | MR

[10] Eremin I.I., Mazurov V.D., Nestatsionarnye protsessy matematicheskogo programmirovaniya, Nauka, M., 1979, 288 pp. | MR

[11] Eremin I.I., “Dvoistvennost dlya nesobstvennykh zadach lineinogo programmirovaniya”, Mat. zametki, 32:2 (1982), 229–238 | MR | Zbl

[12] Eremin I.I., Mazurov V.D., Astafev N.N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983, 336 pp. | MR

[13] Eremin I.I., Protivorechivye modeli optimalnogo planirovaniya, Nauka, M., 1988, 160 pp. | MR

[14] Eremin I.I., Lineinaya optimizatsiya i sistemy lineinykh neravenstv, Akademiya, M., 2007, 256 pp.

[15] Eremin I.I., “Avtorskie rezultaty po problematike matematicheskogo programmirovaniya v retrospektive”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14:2 (2008), 58–66 | Zbl

[16] Eremin I.I., Popov L.D., “Vnutrennie shtrafnye funktsii i dvoistvennost v lineinom programmirovanii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18:3 (2012), 83–89

[17] Erokhin V.I., “Matrichnaya korrektsiya dvoistvennoi pary nesobstvennykh zadach lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 47:4 (2007), 587–601 | MR | Zbl

[18] Erokhin V.I., Krasnikov A.S., Khvostov M.N., “O dostatochnykh usloviyakh razreshimosti zadach lineinogo programmirovaniya pri matrichnoi korrektsii ikh ogranichenii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19:2 (2013), 144–156 | MR

[19] Skarin V.D., “O primenenii metoda nevyazki dlya korrektsii protivorechivykh zadach vypuklogo programmirovaniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:2 (2014), 268–276 | MR

[20] Tikhonov A.N., “O priblizhennykh sistemakh lineinykh algebraicheskikh uravnenii”, Zhurn. vychisl. matematiki i mat. fiziki, 20:6 (1980), 1373–1383 | MR | Zbl