Geodesic
Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1103-1112 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We examine the convergence rate of approximations generated by Tikhonov's scheme as applied to ill-posed constrained optimization problems with general smooth functionals on a convex closed subset of a Hilbert space. Assuming that the solution satisfies a source condition involving the second derivative of the cost functional and depending on the form of constraints, we establish the convergence rate of the Tikhonov approximations in the cases of exact and approximately specified functionals. 
@article{ZVMMF_2017_57_7_a2,
     author = {M. Yu. Kokurin},
     title = {Convergence rate estimates for {Tikhonov's} scheme as applied to ill-posed nonconvex optimization problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1103--1112},
     year = {2017},
     volume = {57},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a2/}
}
TY  - JOUR
AU  - M. Yu. Kokurin
TI  - Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1103
EP  - 1112
VL  - 57
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a2/
LA  - ru
ID  - ZVMMF_2017_57_7_a2
ER  - 
%0 Journal Article
%A M. Yu. Kokurin
%T Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1103-1112
%V 57
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a2/
%G ru
%F ZVMMF_2017_57_7_a2
M. Yu. Kokurin. Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1103-1112. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a2/

[1] Vasilev F. P., Metody resheniya ekstremalnykh zadach. Zadachi minimizatsii v funktsionalnykh prostranstvakh, regulyarizatsiya, approksimatsiya, Nauka, M., 1981

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

[3] Kokurin M. Yu., “O vypuklosti funktsionala Tikhonova i iterativno regulyarizovannykh metodakh resheniya neregulyarnykh nelineinykh operatornykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 50:4 (2010), 651–664 | Zbl

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

[5] Engl H. W., Hanke M., Neubauer A., Regularization of inverse problems, Kluwer, Dordrecht, 2000 | MR

[6] Morozov V. A., “Otsenki tochnosti regulyarizatsii nelineinykh neustoichivykh zadach”, Zh. vychisl. matem. i matem. fiz., 35:9 (1995), 1420–1428 | Zbl

[7] Fitzpatrick S., Phelps R. R., “Differentiability of the metric projection in Hilbert space”, Trans. Amer. Math. Soc., 270 (1982), 483–501 | DOI | MR | Zbl

[8] Holmes R. B., “Smoothness of certain metric projections on Hilbert space”, Trans. Amer. Math. Soc., 184 (1973), 87–100 | DOI | MR

[9] Kokurin M. Yu., “Usloviya istokopredstavimosti i stepennye otsenki skorosti skhodimosti v skheme Tikhonova dlya resheniya nekorrektnykh ekstremalnykh zadach”, Izv. vuzov. Matem., 2014, no. 7, 72–82

[10] Kokurin M. Yu., “O reduktsii variatsionnykh neravenstv s neregulyarnymi operatorami na share k regulyarnym operatornym uravneniyam”, Izv. vuzov. Matem., 2013, no. 4, 32–41

[11] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Fizmatlit, M., 2005