101.804 AKNUM Optimization and shape optimization with partial differential equations
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2022W, SE, 2.0h, 3.0EC
Quinn ECTS survey


  • Semester hours: 2.0
  • Credits: 3.0
  • Type: SE Seminar
  • Format: Presence

Learning outcomes

After successful completion of the course, students are able to understand and solve shape optimization problems and/or optimal control problems contstrained by partial differential equations. Students will have gained an overview over optimisation and shape optimisation with partial differential equations. 

Subject of course

We discuss selected topics in optimisation and shape optimisation with partial differential equations. The focus is on both theory and numerics and possible topics can be

  • shape optimization with shape manifolds
  • shape spaces
  • nonsmooth shape optimization
  • quasi-Newton methods
  • shape optimization with the Minkowski sum
  • semi-smooth Newton methods

Applications of shape optimization are for instance car and aircraft design, electrical machines, conductor design or medical imaging.

Teaching methods

Presentation and if applicable implementation of algorithms

Mode of examination


Additional information


First meeting: Tuesday, 11.10.2022 Sem.R. DA grün 06A

Please consider the plagiarism guidelines of TU Wien when writing your seminar paper: Directive concerning the handling of plagiarism (PDF)



Course dates

Tue11:00 - 12:0011.10.2022Sem.R. DA grün 06A Optimierung und Formoptimierung mit partiellen Differentialgleichungen

Examination modalities

successful presentation

Course registration

Not necessary


Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Mandatory elective


  • Tröltzsch - optimale steuerung partieller differentialgleichungen
  • Delfour/Zolesio - Shape and geometries
  • Ito/Kunisch -  Lagrange Multiplier Approach to Variational Problems and Applications
  • Henro/Pierre - Optimisation de forme
  • Nocedal/Wright - Numerical Optimization
  • Sepulchre, Absil, Mahony - Optimization algorithm on matrix manifolds
  • Kanzow, Geiger - Theorie und Numerik restringierter Optimierungsaufgaben

Previous knowledge

PDE and Numerik; for topics involving manifolds differential geometry is recommended


if required in English