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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 1, Pages 12–22
DOI: https://doi.org/10.31857/S0044466922010033 (Mi zvmmf11341) 		 
Optimal control

Stable solution of a quadratic minimization problem with a nonuniformly perturbed operator by applying a regularized gradient method

L. A. Artem'eva, A. A. Dryazhenkov, M. M. Potapov

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466922010033
Abstract: A regularized gradient method is proposed for stable solution of a quadratic minimization problem under nonconventional information conditions when the error levels in a specified exact linear operator are known only in weakened norms. The convergence of the method with respect to the argument in the norm of the original space is proved. An example is given that explains in which situations the method can be applied.
Key words: quadratic minimization problem, gradient method, regularization, approximate data.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК 3539.2019.1
Russian Foundation for Basic Research 18-31-00391
This work was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics, by a grant from the President of the Russian Federation (project no. MK 3539.2019.1), and by the Russian Foundation for Basic Research (project no. 18-31-00391).
Received: 23.03.2021
Revised: 23.03.2021
Accepted: 17.09.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 1, Pages 10–19
DOI: https://doi.org/10.1134/S0965542522010031
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: L. A. Artem'eva, A. A. Dryazhenkov, M. M. Potapov, “Stable solution of a quadratic minimization problem with a nonuniformly perturbed operator by applying a regularized gradient method”, Zh. Vychisl. Mat. Mat. Fiz., 62:1 (2022), 12–22; Comput. Math. Math. Phys., 62:1 (2022), 10–19
Citation in format AMSBIB
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\paper Stable solution of a quadratic minimization problem with a nonuniformly perturbed operator by applying a regularized gradient method
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\yr 2022
\vol 62
\issue 1
\pages 12--22
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