Optimierung C im WS 2022/2023
Prof. Dr. Michael Herty
Dr. Niklas Kolbe
Questions can be addressed to: kolbe "at" igpm.rwth-aachen.de ✉
The lecture and exercise classes are held in English.
|Lecture (Dr. N. Kolbe)||Mon, 10:30 - 12:00
Tue, 12:30 - 14:00
|149 (main building, first floor)
149 (main building, first floor)
|Exercise (Dr. E. Iacomini and Dr. C. Segala)||Wed, 16:30 - 18:00||149 (main building, first floor)|
Course contentsThis course is concerned with constrained optimization problems over finite- and infinite spaces. Such problems arise among others in the optimal design of airfoils and the control of compressors in networks of gas pipelines. Typically constrained minimization problems are considered, where constraints are often given by partial differential equations. In the lecture we will take a rigorous approaches to these problems using functional analysis and discuss properties and optimality systems in specific examples with partial differential equations. Concepts from finite optimization will be transferred to the infinite case.
The course moreover covers:
- Differentiation in Banach spaces
- Optimal control problems (e.g., Pontryagin's maximum principle, Hamilton-Jacobi Belmann equation)
- Optimization with partial differential equations (e.g., variational problems, Lagrange multipliers, duality formulations)
- Current related research topics (e.g. dynamical programming, shape optimization)
Students can register for the course in RWTHonline. After registration participants automatically get access to the course page inRWTHmoodle where more information is provided and the course is organized.
- Luenberger: Optimization in Vector Spaces, Wiley , 1969
- Tröltzsch: Optimierung mit partiellen Differentialgleichungen , Vieweg, 2002
- Lions: Optimal Control of Systems , Springer, 1971
Further literature will be announced in the lecture.