Stochastic Optimization Lecture (Stochastische Optimierung)

General Information:

Content:

In this module students learn about the theory and the methods of stochastic optimization. The theory is complemented by a range of real-world examples with a focus on applications in energy trading and finance. Along with the examples an introduction to software tools is given that enables students to solve stochastic optimization problems. The required mathematical tools will be introduced along the way.
The module contents span the theory of stochastic optimization (two-stage and multi-stage), numerical solution methods, the treatment of risk via risk measures in stochastic optimization, as well as sampling based approaches.
In particular, topics of the course include but are not limited to

• What is stochastic optimization
• Two-stage linear stochastic optimization with recourse
• Computational methods
• Monte-Carlo methods
• Multi-stage models
• Risk measures in stochastic optimization

The module combines several learning methods.
To facilitate a better understanding of the subject the course is divided into lectures and a lab (excercise). In the lectures theory is presented which is subsequently applied by students in homework assignments using MATLAB. The solutions are handed in and students can volunteer to present their solutions in the lab. In private reading, students complement the knowledge from the lecture with additional methods relevant for solving the cases. Students reflect on the theory and their applicability in class and during class discussion. By working on real world stochastic optimization problems, handling actual data, and designing numerical solution approaches as well as engaging in discussions of their homework solutions, participants get in-depth knowledge about the basics of stochastic optimization.