A Lepskij-type stopping rule for regularized Newton methods

We investigate an a posteriori stopping rule of Lepskij-type for a class of regularized Newton methods and show that it leads to order optimal convergence rates for Hölder and logarithmic source conditions without a priori knowledge of the smoothness of the solution. Numerical experiments show that this stopping rule yields results at least as good as, and in some situations significantly better than, Morozov's discrepancy principle.