Anwendungen von "Variational Analysis" in Optimierung und nichtlinearen Gleichungssystemen

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Variational analysis is a modern discipline of mathematics which has evolved from the classical fieldsof the calculus of variations and convex analysis. It provides, in particular, tools of nonsmooth and set-valued analysis which are employed, e.g.,for analyzing problems of optimization or optimal control. The aim of this research project consists in applying tools from variational analysis to specificquestions from optimization and nonlinear equations. On the one hand, it will be tried to make advanceson the field of "mathematical programs with vanishing problems", a problem class which has turned outto be a powerful framework for several problems from the field of structural optimization and shape design.On the other hand, a new nonsmooth newton method for not necessarily Lipschitz continuous data is supposed to be investigated.