A projection-regularized Newton method for nonlinear ill-posed problems and its application to parameter identification problems with finite element discretization

This paper is concerned with nonlinear ill-posed operator equations F(a) = y (e.g., parameter identification problems) and their approximate solution by a Newton-type method that is regularized by projecting the linearized equation in each Newton step onto a finite-dimensional space (e.g., a finite element space) and by stopping the Newton iteration at an appropriate index. We prove convergence as the iteration index n goes to infinity in the noise-free case and convergence as the data noise level delta goes to zero in the case of noisy data, as well as convergence rates under certain additional conditions.