Geodesic
On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 191-200 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

New results are presented on the construction of exterior penalty functions of increased smoothness in linear programming and on the construction of iterative methods on their basis with automatic matching of their parameters. New constructions, similarly to interior penalty functions, make it possible to use second-order optimization methods and at the same time do not require knowledge of at least one interior admissible point of the original problem for the start of the operation. Moreover, the new penalty functions can also be applied to improper linear programming problems (problems with inconsistent constraint systems), for which they can produce generalized (compromise) solutions. Convergence theorems are proved and data of numerical experiments are presented.
Keywords: linear programming, improper (ill-posed) problems, generalized solutions, penalty functions method, Newton method. 
@article{TIMM_2022_28_4_a17,
     author = {L. D. Popov},
     title = {On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {191--200},
     year = {2022},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a17/}
}
TY  - JOUR
AU  - L. D. Popov
TI  - On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2022
SP  - 191
EP  - 200
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a17/
LA  - ru
ID  - TIMM_2022_28_4_a17
ER  - 
%0 Journal Article
%A L. D. Popov
%T On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions
%J Trudy Instituta matematiki i mehaniki
%D 2022
%P 191-200
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a17/
%G ru
%F TIMM_2022_28_4_a17
L. D. Popov. On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 191-200. http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a17/

[1] Dantsig Dzh., Lineinoe programmirovanie, ego obobscheniya i primeneniya, Progress, M., 1966, 600 pp.

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

[3] Zangvill U. I., Nelineinoe programmirovanie. Edinyi podkhod, Sov. radio, M., 1973, 312 pp. | MR

[4] Polak E., Chislenye metody optimizatsii, Mir, M., 1974, 376 pp.

[5] Eremin I. I., Dokl. AN SSSR, 173:4 (1967), Metod shtrafov v vypuklom programmirovanii

[6] Moiseev N. N., Ivanilov Yu. P., Stolyarova E. M., Metody optimizatsii, Nauka, M., 1978, 351 pp.

[7] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982, 432 pp. | MR

[8] Gill F., Myurrei U., Rait M., Prakticheskaya optimizatsiya, Mir, M., 1985, 509 pp. | MR

[9] Vasilev F.P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988, 552 pp. | MR

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

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

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

[13] 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

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

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

[16] Popov L. D., “Ob odnom prieme povysheniya gladkosti vneshnikh shtrafnykh funktsii v lineinom i vypuklom programmirovanii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 27:4 (2021), 88–101 | MR