Tikhonov regularization under epi-convergent perturbations
type: Item
instance of: scholarly article
title: Tikhonov regularization under epi-convergent perturbations
zbMATH Open document ID: 1008.49018
author: Tullio Zolezzi
published in: Ricerche di Matematica
publication date: 2002-12-17T00:00:00Z
review text: Global optimization problems in a Banach space with perturbed data are considered. At each stage an approximate minimization is performed by applying Tikhonov regularization to every perturbed problems. Known results show that Tikhonov regularization provides strongly convergent minimizing sequences (up to subsequences) in case of perturbed data converging uniformly. In this paper, the author generalizes those results to nonconvex problems in case of epi-convergent perturbations of the original problem, making use of the notion of epi-distance, and applies the new results to ill-posed problems under perturbations. In the end, a quantitative estimate of the rate of convergence of the regularization assuming convexity of the data is obtained.
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 65J20
zbMATH DE Number: 1846795
zbMATH Keywords: perturbed problems
zbMATH Keywords: epi-convergent perturbations
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: global optimization problems
reviewed by: Rita Pini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1846795