Geodesic
Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 3, pp. 138-155
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, the author continues his research on the modification and adaptation of classical methods of the central path in order to apply them to the analysis of improper problems of linear programming. In the new constructions presented in the paper, in contrast to those developed earlier, it becomes possible to apply second-order optimization methods. Moreover, there is no need to specify in advance the type of impropriety of the problem being solved. Convergence theorems for the constructed methods are given, a meaningful interpretation of the obtained generalized solution is provided, and the results of numerical experiments are presented.
Keywords: linear programming, improper problems, generalized solutions, barrier function method, regularization. 
@article{TIMM_2023_29_3_a8,
     author = {L. D. Popov},
     title = {Barriers and symmetric regularization of the {Lagrange} function in the analysis of improper linear programming problems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {138--155},
     year = {2023},
     volume = {29},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/}
}
TY  - JOUR
AU  - L. D. Popov
TI  - Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2023
SP  - 138
EP  - 155
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/
LA  - ru
ID  - TIMM_2023_29_3_a8
ER  - 
%0 Journal Article
%A L. D. Popov
%T Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems
%J Trudy Instituta matematiki i mehaniki
%D 2023
%P 138-155
%V 29
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/
%G ru
%F TIMM_2023_29_3_a8
L. D. Popov. Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 3, pp. 138-155. http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/

[1] Eremin I.I., “Dvoistvennost dlya nesobstvennykh zadach lineinogo i vypuklogo programmirovaniya”, Dokl. AN SSSR, 256:2 (1981), 272–276 | MR | Zbl

[2] Eremin I.I., Mazurov Vl.D., Astafev N.N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983, 336 pp.

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

[4] Morozov V.A., “O psevdoresheniyakh”, Zhurn. vychisl. matematiki i mat. fiziki, 9:6 (1969), 1387–1391 | MR | Zbl

[5] Kochikov I.V., Matvienko A.N., Yagola A.G., “Obobschennyi printsip nevyazki dlya resheniya nesovmestnykh uravnenii”, Zhurn. vychisl. matematiki i mat. fiziki, 24:7 (1984), 1087–1090 | MR | Zbl

[6] Issledovaniya po nesobstvennym zadacham optimizatsii, cb. nauch. statei, UrO AN SSSR, Sverdlovsk, 1988, 78 pp.

[7] Parametricheskaya optimizatsiya i metody approksimatsii nesobstvennykh zadach matematicheskogo programmirovaniya, cb. nauch. statei, UNTs AN SSSR, Sverdlovsk, 1985, 136 pp.

[8] Skarin V.D., “Ob odnom podkhode k analizu nesobstvennykh zadach lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 26:3 (1986), 439–448 | MR | Zbl

[9] Neregulyarnaya dvoistvennost v matematicheskom programmirovanii, cb. nauch. statei, UNTs AN SSSR, Sverdlovsk, 1990, 78 pp.

[10] Skarin V.D., “O metode barernykh funktsii i algoritmakh korrektsii nesobstvennykh zadach vypuklogo programmirovaniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14:2 (2008), 115–128, Ekaterinburg | MR | Zbl

[11] Popov L.D., “Poisk obobschennykh reshenii nesobstvennykh zadach lineinogo i vypuklogo programmirovaniya s pomoschyu barernykh funktsii”, Izv. Irkut. gos. un-ta. Ser. Matematika, 4:2 (2011), 134–146 | Zbl

[12] 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

[13] Popov L.D., “Primenenie barernykh funktsii dlya optimalnoi korrektsii nesobstvennykh zadach lineinogo programmirovaniya 1-go roda”, Avtomatika i telemekhanika, 2012, no. 3, 3–11 | Zbl

[14] Fiakko A., Mak–Kormik G., Nelineinoe programmirovanie. Metody posledovatelnoi bezuslovnoi minimizatsii, Mir, M., 1972, 240 pp. | MR

[15] Eremin I.I., Astafev N.N., Vvedenie v teoriyu lineinogo i vypuklogo programmirovaniya, Nauka, M., 1976, 192 pp.

[16] Rokafellar R.T., Vypuklyi analiz, Mir, M., 1973, 472 pp.

[17] Roos C., Terlaky T., Vial J.-Ph., Theory and algorithms for linear optimization, John Wiley Sons Ltd., Chichester, 1997, 484 pp. | MR