Optimierung C kompakt im WS 2023/2024

Dr. Niklas Kolbe
Dr. Chiara Segala

Questions can be addressed to: kolbe "at" igpm.rwth-aachen.de ✉

The lectures and exercise classes are held in English.


Course Time Room
Lecture Tue, 10:30 - 12:00 tba
Exercise Wed, 08:30 - 10:00, biweekly tba

Course contents

This 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 in RWTHmoodle 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.