Abstract
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 105005 |
| Journal | Inverse Problems |
| Volume | 27 |
| Issue number | 10 |
| DOIs | |
| State | Published - Sep 16 2011 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors are grateful to two anonymous referees whose constructive comments have led to an improved presentation. The work of BJ was supported by Award no KUS-C1-016-04, made by the King Abdullah University of Science and Technology (KAUST). A part of the work was carried out during his visit at Graduate School of Mathematical Sciences, The University of Tokyo, and he would like to thank Professor Masahiro Yamamoto for the kind invitation and hospitality.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.