Antrittsvorlesung
Prof. Dr. Constantin Christof, TU Darmstadt

This talk is concerned with the numerical solution of nonsmooth equations by means of Newton's method.
We give an overview of the theory of nonsmooth Newton algorithms and its key concept of Newton differentiability. We further discuss recently obtained results on the Newton differentiability of projections onto sets with box-constraints in Sobolev spaces and their use in the fields of quasi-variational inequalities and inverse homogenization. The talk concludes with numerical experiments which demonstrate the effectiveness of the described algorithms.