Stochastic Optimization

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

After the successful completion of this module, students are able (1) to understand the basic theory of stochastic optimization, (2) to critically reflect the limitations of the theory, (3) to implement solution approaches for stochastic optimization using MATLAB in combination with numerical solvers, (4) to model real-world problems under uncertainty as stochastic optimization problems that can be treated with the methods introduced in the course, (5) to communicate the results to a scientific audience.

Grading is based on of a final exam (60%), written presentation of the results obtained for the homework (40%), and bonus points are awarded for participation in discussions in the lecture and the lab. With this voluntary mid-term assignment students can improve their module grade. The homework during the semester serves to assess the ability to apply stochastic optimization to real world problems. By this method, the students continually reflect about the theory presented in class and learn to translate theoretical knowledge into practical solutions. The in-depth knowledge of the theory of stochastic optimization and the critical reflection of its limitations are assessed in a final written exam focussing on the theoretical knowledge. Moreover, the students can prove their ability to relate these theoretical results to real world problems. The presentation and discussion of the homework in the lab sessions measure students' ability to structure and present their results, connect them with state-of-the-art methods and theories, and present them in a scientific way.

Knowledge of basic linear optimization and basic probability theory would be an advantage. The required theory is reviewed in the class.

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.