# A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems

## TL;DR

This paper investigates a priori parameter choice strategies in Tikhonov regularization for non-linear ill-posed problems, focusing on cases where solutions lack finite smoothness penalties, and establishes optimal convergence rates.

## Contribution

It extends previous work to non-linear problems, providing optimal convergence rates for a priori parameter choices even with oversmoothing penalties.

## Key findings

- Established optimal convergence rates for non-linear problems
- Analyzed cases with non-finite penalty solutions
- Extended linear case results to non-linear settings

## Abstract

We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study 'Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales'. Inverse Problems 34(1), 2018, by the same authors. Optimal order convergence rates are established for the specific a priori parameter choice, as used for the corresponding linear equations.