This article is cited in 3 papers

Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems

M. Yu. Kokurin

Mari State University, 1 Lenin sq., Yoshkar-Ola, 424001 Russia

Abstract: 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.

UDC: 517.988

Received: 20.01.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:6, 51–59

Bibliographic databases:

• 
•