Geodesic
Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 60-69

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We investigate a rate of convergence of estimates for approximations generated by Tikhonov's scheme for solving ill-posed optimization problems with smooth functionals under a structural nonlinearity condition in a Hilbert space, in the cases of exact and noisy input data. In the noise-free case, we prove that the power source representation of the desired solution is close to a necessary and sufficient condition for the power convergence estimate having the same exponent with respect to the regularization parameter. In the presence of a noise, we give a parameter choice rule that leads for Tikhonov's scheme to a power accuracy estimate with respect to the noise level.
Keywords: ill-posed optimization problem, Hilbert space, Tikhonov's scheme, rate of convergence, sourcewise representability condition. 
@article{IVM_2017_6_a6,
     author = {M. Yu. Kokurin},
     title = {Necessary and sufficient conditions for power convergence rate of approximations in {Tikhonov's} scheme for solving ill-posed optimization problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--69},
     publisher = {mathdoc},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_6_a6/}
}
TY  - JOUR
AU  - M. Yu. Kokurin
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%A M. Yu. Kokurin
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%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 60-69
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%I mathdoc
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%G ru
%F IVM_2017_6_a6
M. Yu. Kokurin. Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 60-69. http://geodesic.mathdoc.fr/item/IVM_2017_6_a6/