Theorie und Verfahren der nichtglatten Optimierung (M21): Obstacle Problems and optimal control
Description: We begin with a study of elliptic variational inequalities (Vis) of obstacle type. Starting with existence results and basic properties and theory, we’ll move onto approximating Vis by solutions of PDEs and related concepts. Sensitivity analysis and directional differentiability of solution maps of Vis will also be touched on, as well as optimal control of Vis: existence of controls and stationarity conditions in particular. The final part of the course will cover quasi-variational inequalities (QVIs), an exciting generalisation of Vis with many interesting properties and an active area of research. Real-world applications will also be given.