Regularization methods for solving nonlinear ill-posed inverse problems

This project is to investigate nonlinear inverse problems which in general are ill-posed in the sense that their solutions do not depend continuously on the data. In order to obtain stable approximation to the true solution when noisy data is used, one has to use regularization methods which replace the original problem by a family of well-posed problems. These methods always involve some parameters which should be chosen carefully to get optimal accuracy and their choice as well as convergence properties of the methods is a central topic. We will use optimization tools and Newton type procedures to develop various efficient regularization solvers and design parameter choice rules yielding order optimal convergence rates.