Preprint
On existence of a variational regularization parameter under Morozov's discrepancy principle
ArXiV.org
Cornell University
06/12/2025
DOI: 10.48550/arxiv.2506.11397
Abstract
Morozov's discrepancy principle is commonly adopted in Tikhonov
regularization for choosing the regularization parameter. Nevertheless, for a
general non-linear inverse problem, the discrepancy
$\|F(x_{\alpha}^{\delta})-y^{\delta}\|_Y$ does not depend continuously on
$\alpha$ and it is questionable whether there exists a regularization parameter
$\alpha$ such that $\tau_1\delta\leq
\|F(x_{\alpha}^{\delta})-y^{\delta}\|_Y\leq \tau_2 \delta$ $(1\le
\tau_1<\tau_2)$. In this paper, we prove the existence of $\alpha$ under
Morozov's discrepancy principle if $\tau_2\ge (3+2\gamma)\tau_1$, where
$\gamma>0$ is a parameter in a tangential cone condition for the nonlinear
operator $F$. Furthermore, we present results on the convergence of the
regularized solutions under Morozov's discrepancy principle. Numerical results
are reported on the efficiency of the proposed approach.
Details
- Title: Subtitle
- On existence of a variational regularization parameter under Morozov's discrepancy principle
- Creators
- Liang DingLong Li - Northeast Forestry UniversityWeimin HanWei Wang - Jiaxing University
- Resource Type
- Preprint
- Publication Details
- ArXiV.org
- DOI
- 10.48550/arxiv.2506.11397
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 06/12/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984832090202771
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