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

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...

Full description

Saved in:
Bibliographic Details
Published in:Russian mathematics 2017-06, Vol.61 (6), p.51-59
Main Author: Kokurin, M. Yu
Format: Article
Language:English
Subjects:
Convergence
Economic models
Functionals
Hilbert space
Ill posed problems
Mathematics
Mathematics and Statistics
Noise
Optimization
Regularization
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X1706007X