Dr. Andreas Gründinger

The lecture deals with common mathematical models of optimization and introduces algorithms and methods based on these optimization models, which are also used for problems in machine learning applications, e.g., automated driving functions.

Motivation:

Numerical algorithms are the basis for all automation in the digital age. Each of these algorithms serves to solve (at least) one objective, e.g. minimizing travel time in navigation system route planning or minimizing errors in image recognition. The lecture deals with mathematical models and the associated solution methods for such and other optimization problems that are amongst others used in the course of machine learning.

The lecture provides an introduction to the subject area of mathematical optimization. This enables students to classify mathematical optimization problems based on the properties of the objective function and constraints. Depending on the selected class, classical solution methods and their implementation are discussed. In exercises and examples, the techniques learned are applied to common tasks in the field of machine learning, e.g., basic regularization, classification, the training of neural networks for image recognition and calculating bounds on the optimal values.

More Motivation ;-)

It is human nature to want to understand how complex processes (problems) work in order to be able to exploit them for our own benefit. Engineers in particular are often faced with the question "How can I improve the way things work?" Over time, it is therefore a natural learning process to deal with the modeling and structure of optimization problems in order to know the classical solution methods for common problems.

Prerequisites:

The lecture is aimed at Master's students. Basic prerequisites are knowledge of linear algebra and stochastics. The relevant results from these areas are repeated in the lecture.

Aim of the Lecture:

Through active participation in the lecture and practical exercises on applied optimization, students learn to ...

• differentiate and classify optimization problems with regard to linearity/convexity of the objective function and the constraints.
• apply solution methods for common convex optimization problems.
• develop methods for optimization tasks in the context of automated driving functions.

Applications include, for example ...

• filter calculation in signal processing, communication, image recognition, and so forth.
• the training of neural networks in machine learning,
• solving regularisation methods and classification problems without neural networks.
• getting bounds of the optimal values and approximation for complex optimisation problems.