A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems
Provides theoretical convergence guarantees for a class of non-linear inverse problems where solution smoothness is insufficient, benefiting researchers in inverse problems and regularization theory.
This paper establishes optimal order convergence rates for Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems under a specific a priori parameter choice, extending previous results from linear to non-linear equations.
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.