Bernd Hofmann, Peter Mathé: Parameter choice in Banach space regularization under variational inequalities

Author(s):

Bernd Hofmann
Peter Mathé

Title:

Bernd Hofmann, Peter Mathé: Parameter choice in Banach space regularization under variational inequalities

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 05, 2012

Mathematics Subject Classification:

65J20	[]
47J06	[]
47A52	[]
49J40	[]

Abstract:

The authors study parameter choice strategies for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depends on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepski\u\i{} principle. For the convenience of the reader the authors review in an appendix a few instances where the validity of a variational inequality can be established.

Keywords:

Nonlinear ill-posed problems, Banach space regularization, convergence rates, variational inequalities, parameter choice rules

Language:

English

Publication time:

04/2012