Anwendungen von "Variational Analysis" in Optimierung und nichtlinearen Gleichungssystemen

变分分析是由变分学和凸分析等经典领域发展而来的一门现代数学学科。它特别提供了非光滑分析和集值分析的工具，用于分析最优化或最优控制问题。本研究项目的目的在于将变分分析的工具应用于优化和非线性方程等具体问题。一方面，它将尝试在“具有消失问题的数学程序”领域取得进展，这个问题类已经成为结构优化和形状设计领域的几个问题的强大框架。另一方面，研究了一种新的非光滑牛顿方法，该方法适用于不一定连续的Lipschitz数据。

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.