# Numerical Analysis of State-Constrained Optimal Control Problems for PDEs

### From DFG-SPP 1253

## Project leader

Institut für Mathematik

TU Berlin

Tel: 030 31479-688

Fax: 030 314-79-688

Email: troeltzsch@math.tu-berlin.de

Homepage:

## DFG funded assistant

Ira Neitzel (TU Berlin)

neitzel@math.tu-berlin.de

## Description

- Optimal control of nonlinear systems of PDEs with state constraints
- Focus on semi-linear parabolic boundary control problems
- Regularization techniques of Lavrentiev-type
- Semi-infinite optimization

The project is a contribution to the optimal control of nonlinear systems of PDEs with pointwise state-constraints. The work is focussed on two aspects of associated numerical methods and their analysis. In a first topic, regularization techniques of Lavrentiev type will be studied to solve state-constrained problems. Exemplarily, special emphasis is placed on semilinear parabolic equations with boundary control and state constraints in the domain. A second part of the project is devoted to the case where the controls are given by a linear combination of finitely many ansatz functions, where the coefficients are constant or may depend on time. This situation is characteristic for many applications in practice and leads to semi-infinite optimization problems.