###### News

The lecture on 15.11.2023 is replaced by the exercise class on the same day.###### Content

Nonsmooth equations and optimization problems nowadays play an indispensable role in many applications such as optimal control with partial differential equation constraints, imaging and datascience. In this course we will discuss the semi-smooth Newton method which is suitable to approach many of these problems and has in addition good properties such as fast local convergence and mesh independence.###### Dates

Tuesday 11:00 - 13:00, Room 2.006 RUD25Wednesday 13:00 - 15:00, Room 1.114 RUD25

###### Syllabus

The following topics will be covered:- Recap of the classical Newton method
- Semismooth Newton method
- Semismooth Newton in finite dimensions
- Semismooth Newton in infinite dimensions
- Globalization techniques
- Path following
- Mesh independence

- Applications
- Optimal control of PDEs with control constraints
- Regularization for problems with low multiplier regularity
- Image processing

###### Literature

There are lecture notes that serve as the main reference for the course. However, the following resources will also be helpful:- Facchinei, Francisco and Pang, Jong-shi: Finite-Dimensional Variational Inequalities and Complementarity Problems. First edition, 2003
- Ulbrich, Michael: Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces. First edition, 2011
- Hinze, Michael, Pinnau, Rene, Ulbrich, Michael and Ulbrich, Stefan: Optimization with PDE Constraints. First edition, 2009

###### Contact

Prof. Michael Hintermüller, michael.hintermueller[at]wias-berlin.deClemens Sirotenko, sirotenko[at]wias-berlin.de

###### Links

- Prof. Michael Hintermüller's webpage
- Clemens Sirotenko's webpage
- Department of Mathematics
- Mathematics students' council