Geodesic
On the application of the residual method for the correction of inconsistent problems of convex programming
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 268-276 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

For the correction of a convex programming problem with potentially inconsistent constraint system (an improper problem), we apply the residual method, which is a standard regularization procedure for ill-posed optimization models. Further, a problem statement typical for the residual method is reduced to the minimization problem for an appropriate penalty function. We apply two classical penalty functions: the quadratic penalty function and the Eremin–Zangwill exact penalty function. For each of the approaches, we establish convergence conditions and estimates for the approximation error.
Keywords: convex programming, improper problem, residual method, penalty function methods.
Mots-clés : optimal correction 
@article{TIMM_2014_20_2_a22,
     author = {V. D. Skarin},
     title = {On the application of the residual method for the correction of inconsistent problems of convex programming},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {268--276},
     year = {2014},
     volume = {20},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a22/}
}
TY  - JOUR
AU  - V. D. Skarin
TI  - On the application of the residual method for the correction of inconsistent problems of convex programming
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2014
SP  - 268
EP  - 276
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a22/
LA  - ru
ID  - TIMM_2014_20_2_a22
ER  - 
%0 Journal Article
%A V. D. Skarin
%T On the application of the residual method for the correction of inconsistent problems of convex programming
%J Trudy Instituta matematiki i mehaniki
%D 2014
%P 268-276
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a22/
%G ru
%F TIMM_2014_20_2_a22
V. D. Skarin. On the application of the residual method for the correction of inconsistent problems of convex programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 268-276. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a22/

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

[3] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 288 pp. | MR

[4] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981, 400 pp. | MR

[5] Skarin V. D., “O metode regulyarizatsii dlya protivorechivykh zadach vypuklogo programmirovaniya”, Izv. vuzov. Matematika, 1995, no. 12, 81–88 | MR | Zbl

[6] Popov L. D., “Kombinirovannye shtrafy i obobschennye resheniya nesobstvennykh zadach lineinogo i vypuklogo programmirovaniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 3, 2010, 217–226

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

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

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

[10] Eremin I. I., “Metod “shtrafov” v vypuklom programmirovanii ”, Dokl. AN SSSR, 173:4 (1967), 748–751 | MR | Zbl

[11] Eremin I. I., “K metodu shtrafov v matematicheskom programmirovanii”, Dokl. RAN, 346:4 (1996), 459–461 | MR | Zbl

[12] Skarin V. D., “O primenenii odnogo metoda regulyarizatsii dlya korrektsii nesobstvennykh zadach vypuklogo programmirovaniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18, no. 3, 2012, 230–241