Topics for projects and master theses – Dietmar Hömberg
I am a member of Weierstrass Institute and Technische Universität Berlin and have an adjunct position here at NTNU in the new Optimization group. My physical presence at NTNU is limited, so supervision has to be done at least to some extend via Skype. Another possibility is to combine work on the project or MsC thesis with an Erasmus stay at TU Berlin. Besides the fact that Berlin is a kaleidescope of cultural, social and historical elements (not to mention partying ), it is one of the best places for Applied Mathematics in Germany.
Topics for projects and theses may focus on theoretical or numerical aspects or on a case study from engineering or life sciences.
For students with some knowledge in nonlinear optimization, e.g., from the course Optimization Theory some topics I could offer are
- non-smooth optimization (optimality conditions, numerical methods)
- vector-valued optimization (again with focus on theory or numerics)
- deterministic and non-deterministic methods for global optimization
- an application case study
- further selected topics in nonlinear optimization
For students with knowledge in Variational Calculus and Optimal Control, topics could be applied control problems from engineering, biology, sports, etc. Here, I would expect that the model is described, the control problem is formulated, necessary optimality conditions are derived followed by some numerical simulations. Depending on personal preference the focus can be on one or two of the tasks.
A very nice new project for optimal control which is really applied has been suggested by Anders Skonhoft, Department of Economics, NTNU. It is about an optimal control problem related to a predator prey model for moose and wolf with interesting consequences for ecology and economy.
If you are interested in one of these topics send me an email.