Seminar Mathematische Optimierung (4 ECTS)

für Master Wirtschaftsmathematik
Lecturer: Prof. Dr. Claudia Schillings, Dr. Vesa Kaarnioja

Dates

Monday, 8:30 – 11:45 h in B6, 23-25- A304 (block seminar in the period 07.10.2019 – 18.11.2019)

To register for the seminar, please send an email to c.schillings(at)uni-mannheim.de. Please note that the seminar will take place on Mondays (instead of Fridays!).

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Content

High-dimensional numerical integration plays a central role in contemporary applied mathematics. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task.

This seminar course focuses on the sparse grid approach of constructing efficient and generalizable integration and approximation routines for high-dimensional problems. Sparse grids constitute a useful toolbox that can be applied for a wide range of problems.

In this seminar course, we start with an introductory lecture about the topic starting with the original sparse grid formulation invented by S.~A. Smolyak (1963) and work our way to the modern understanding of sparse grids, including dimension-adaptive formulations capable of solving challenging integration and approximation problems involving thousands or even tens of thousands of variables. During the seminar course, the seminar participants will present their findings about a topic related to a contemporary application of sparse grids.

Learning Outcoms

The objective of this course is learning to recognize when high-dimensional integration and approximation problems arise in practice. You will learn about cutting edge numerical methods that are needed for solving these problems, and you will learn to implement this knowledge in practice. The methods discussed during this course are very useful for doing research in uncertainty quantification, an active and fast-growing field of research.

Prerequisites and passing the course

Linear algebra and calculus of several variables. Some knowledge about PDEs and MATLAB (or other programming languages) is recommended.

Making a presentation and active participation in the seminar are required for passing the course.