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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 7, Pages 1103–1112 (Mi zvmmf10584)  

This article is cited in 1 scientific paper (total in 1 paper)

Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems

M. Yu. Kokurin

Mari State University, Yoshkar-Ola, Russia

Abstract: 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.

Key words: ill-posed optimization problem in a Hilbert space, convex closed set, Tikhonov's scheme, convergence rate, source condition.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00039_a


DOI: https://doi.org/10.7868/S0044466917070109

Full text: PDF file (172 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:7, 1101–1110

Bibliographic databases:

UDC: 519.642.8
Received: 19.01.2016

Citation: M. Yu. Kokurin, “Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1103–1112; Comput. Math. Math. Phys., 57:7 (2017), 1101–1110

Citation in format AMSBIB
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\by M.~Yu.~Kokurin
\paper Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 7
\pages 1103--1112
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\crossref{https://doi.org/10.7868/S0044466917070109}
\elib{https://elibrary.ru/item.asp?id=29404219}
\transl
\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 7
\pages 1101--1110
\crossref{https://doi.org/10.1134/S0965542517070090}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Yu. Kokurin, “Solution of ill-posed nonconvex optimization problems with accuracy proportional to the error in input data”, Comput. Math. Math. Phys., 58:11 (2018), 1748–1760  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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