Geodesic
On the choice of parameters in the quasisolution method for the correction of improper convex programs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 3, pp. 187-197 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper is devoted to finding approximation solutions of improper convex programs. For such programs, a correction model is considered in the form of the problem of minimizing the objective function of the original problem on the set of extremal points of a penalty function, which aggregates the inconsistent constraints. For the penalty function, the Eremin–Zangwill exact penalty function is chosen. Under an approximately given input, a generalized solution of the improper convex program is obtained by applying the quasisolution method known in the theory of ill-posed problems. Estimates characterizing the quality of the correction are given. Iterative schemes implementing this approach are proposed.
Keywords: convex programming, improper problem, exact penalty function method, quasisolution method.
Mots-clés : optimal correction 
@article{TIMM_2020_26_3_a15,
     author = {V. D. Skarin},
     title = {On the choice of parameters in the quasisolution method for the correction of improper convex programs},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {187--197},
     year = {2020},
     volume = {26},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2020_26_3_a15/}
}
TY  - JOUR
AU  - V. D. Skarin
TI  - On the choice of parameters in the quasisolution method for the correction of improper convex programs
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2020
SP  - 187
EP  - 197
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2020_26_3_a15/
LA  - ru
ID  - TIMM_2020_26_3_a15
ER  - 
%0 Journal Article
%A V. D. Skarin
%T On the choice of parameters in the quasisolution method for the correction of improper convex programs
%J Trudy Instituta matematiki i mehaniki
%D 2020
%P 187-197
%V 26
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2020_26_3_a15/
%G ru
%F TIMM_2020_26_3_a15
V. D. Skarin. On the choice of parameters in the quasisolution method for the correction of improper convex programs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 3, pp. 187-197. http://geodesic.mathdoc.fr/item/TIMM_2020_26_3_a15/

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

[2] Popov L. D., Skarin V. D., “Leksikograficheskaya regulyarizatsiya i dvoistvennost dlya nesobstvennykh zadach lineinogo programmirovaniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 21:3 (2015), 279–291

[3] Skarin V. D., “On the application of the residual method for the correction of inconsistent problems of convex programming”, Proc. Steklov Institute Math., 289, no. Suppl. 1, 2015, S182-S191 | DOI | MR | Zbl

[4] Volkov V. V., Erokhin V. I., Krasnikov A. S., Razumov A. V., Khvatov M. N., “Minimalnaya po evklidovoi norme matrichnaya korrektsiya pary dvoistvennykh zadach lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 57:11 (2017), 1788–1803 | Zbl

[5] Muraveva O. V., “Opredelenie radiusov sovmestnosti i nesovmestnosti sistem lineinykh uravnenii i neravenstv po matrichnoi norme $l1$”, Zhurn. vychisl. matematiki i mat. fiziki, 58:6 (2018), 873–882 | MR | Zbl

[6] Vasilev F. P., Potapov M. M., Artemeva L. A., “Ekstragradientnyi metod korrektsii protivorechivykh zadach lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 58:12 (2018), 1992–1998 | Zbl

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

[8] Vasilev F. P., Metody optimizatsii, Kn. 1, 2, MTsNMO, M., 2011, 1056 pp.

[9] Golub G. N., Hansen P. C., O'Leary D. P., “Tikhonov regularization and total least squares”, SIAM J. Matrix Anal. Appl., 21:1 (1999), 185–194 | DOI | MR | Zbl

[10] Renaut R. A., Guo N., “Efficient algorithms for solution of regularized total least squares”, SIAM J. Matrix Anal. Appl., 26:2 (2005), 457–476 | DOI | MR | Zbl

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

[12] Burke J. V., “An exact penalization viewpoint of constrained optimization”, SIAM J. Contr. Optim., 29:4 (1991), 968–998 | DOI | MR | Zbl

[13] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981, 384 pp. | MR