Globalizing a nonsmooth Newton method via path search

We give a framework for the globalization of a nonsmooth Newton method introduced by B. Kummer. We start with recalling Kummer's approach to convergence analysis of this method and state his results for local convergence. In a second part we give a globalized version of this method. In our approach we use a path-search idea to control the descent. After elaborating the single steps, we analyze and discuss the proof of global convergence resp. of local superlinear or quadratic convergence of the algorithm. We end with illustrating our ideas at some interesting examples.