Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 208-223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An algorithm for solving a quadratic minimization problem on an ellipsoidal set in a Hilbert space is proposed. The algorithm is stable to nonuniform perturbations of the operators. A key condition for its application is that we know an estimate for the norm of the exact solution. Applications to boundary control problems for the one-dimensional wave equation are considered. Numerical results are presented.
@article{ZVMMF_2016_56_2_a3,
     author = {A. A. Dryazhenkov and M. M. Potapov},
     title = {Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {208--223},
     year = {2016},
     volume = {56},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a3/}
}
TY  - JOUR
AU  - A. A. Dryazhenkov
AU  - M. M. Potapov
TI  - Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 208
EP  - 223
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a3/
LA  - ru
ID  - ZVMMF_2016_56_2_a3
ER  - 
%0 Journal Article
%A A. A. Dryazhenkov
%A M. M. Potapov
%T Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 208-223
%V 56
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a3/
%G ru
%F ZVMMF_2016_56_2_a3
A. A. Dryazhenkov; M. M. Potapov. Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 208-223. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a3/

[1] Krnich I., Potapov M. M., “Ob usloviyakh korrektnosti zadach minimizatsii kvadratichnogo funktsionala na ellipsoide i poluprostranstve”, Math. Montisnigri, 1995, no. 4, 27–41 | MR

[2] Jacimović M., Krnić I., Potapov M., “On well-possedness of quadratic minimization problem on elipsoid and polyhedron”, Publications de L'institut Mathematique. Nouvelle Serie, 62:76 (1997), 105–112 | MR | Zbl

[3] Kpnich I., Potapov M. M., “Ob usloviyakh razreshimosti zadach kvadratichnoi minimizatsii s kvadpatichnym i lineinym ogranicheniyami”, Math. Montisnigri, XV (2002), 33–44

[4] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka. Fizmatlit, M., 1995 | MR

[5] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR

[6] Krnich I., Potapov M. M., “Proektsionnaya istokopredstavimost normalnykh reshenii lineinykh uravnenii na vypuklykh mnozhestvakh”, Zh. vychisl. matem. i matem. fiz., 41:9 (2001), 1315–1323 | MR | Zbl

[7] Potapov M. M., “Ustoichivyi metod resheniya lineinykh uravnenii s neravnomerno vozmuschennym operatorom”, Dokl. AN, 365:5 (1999), 596–598 | MR | Zbl

[8] Vasilev F. P., Kurzhanskii M. A., Potapov M. M., Razgulin A. V., Priblizhennoe reshenie dvoistvennykh zadach upravleniya i nablyudeniya, Izd. otdel fakulteta VMK MGU imeni M. V. Lomonosova, M.; MAKS Press, 2010

[9] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[10] Vasilev F. P., Metody optimizatsii, v. 2, MTsNMO, M., 2011

[11] Potapov M. M., Dryazhenkov A. A., “Optimizatsiya porogovogo momenta v neravenstve nablyudaemosti dlya volnovogo uravneniya s kraevym usloviem uprugogo zakrepleniya”, Tr. MIAN, 277, 2012, 215–229 | MR | Zbl

[12] Potapov M. M., Ivanov D. A., “Zadachi dvustoronnego granichnogo upravleniya dlya volnovogo uravneniya na dokriticheskikh promezhutkakh v klassakh silnykh obobschennykh reshenii”, Tr. In-ta matem. i mekh. UrO RAN, 19, no. 4, 2013, 192–202