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. 
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/
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     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},
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     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_6_a6/}
}
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