### **Technische Universität München, Zentrum Mathematik**

# **Case Studies in Nonlinear Optimization**

### **Combined Lecture and Project Work Course**

### **Dr. Sebastian Albrecht**

### **Summer Term 2015**

### Basic Concept- Projects - Schedule - Registration/Preliminary Meeting

# Basic Concept

The description of this module**MA4513**can be found in TUMonline.

This course is a combination of a lecture part and an exercise part where an application example of nonlinear optimization is addressed by a team of three to five students. The lectures provide, on the one hand, mathematical theory and tools to solve the application examples and, on the other hand, cover topics as the organization of team work, the design of posters and the presentation of mathematical content to different target audiences.

The main part of this course are independent studies within a team of students. Consequently, team work and team organization are as important as profound mathematics, programming skills, modeling techniques or presentation skills.

# Projects

Project 1:**Realtime Optimal Control of a Quadcopter**

Controlling an aircraft is a challenging task due to rapid changes of the environment, especially the precise effects of wind are hard to predict. Thus one cannot determine the optimal controls before the take-off and then only replay them during the flight, but one needs to adapt the control strategies continuously during the flight. Therefore, methods of real-time optimization are combined with strategies of model predictive control to control a quadcopter. Project 2:

**Stochastic Optimization in Machine Learning**

Is the object registered by a telescope a quasar? Which tags should be added to a new article or post? In machine learning you usually have huge dataset and given labeled examples the goal is to automatically classify the rest of the dataset. This classification task can be formulated as an optimization problem, but due to its large dimensions special techniques of stochastic optimization are needed to tackle this problem class. Project 3:

**Robust Control of a Car**

In most situations of steering a car the goal is choose controls fulfilling all constraints, e.g., avoiding crashes, and simultaneously optimizing certain cost criteria, e.g., travel time and fuel consumption. However, formulating the problem as an optimal control problem yields solutions which are optimal for specific parameters, but often even small deviations in these parameters result in violation of the constraints. Since the model parameters change considerably, for example, for different terrains and weather conditions, the goal is to determine a robust optimal control that allows to stay feasible for a whole neighborhood of parameters. Project 4:

**Bilevel Optimization in Image Processing**

In image compression one tries to minimize the amount of data to be stored, but keep as much information as possible of the original image. The idea of inpainting compression models is to store only a small number of image pixels and reconstruct the deleted parts by solving an optimization problem. Consequently, the goal is of this project to optimally choose the pixel selection which yields a combination of two optimization problems – a so-called bilevel optimization problem.

# Schedule

**Course Schedule:**

Two time-slots are reserved

**every week**and are used for lectures, internal team presentations (attendance absolutely mandatory) and team meetings with the advisors.

The first meeting was on Monday, April 13th!

Mondays | 10:15 - 11:45 | MI 00.07.014 |
---|---|---|

Wednesdays | 14:15 - 15:45 | MI 00.07.014 |

# Registration

Registration for the case studies in nonlinear optimization 2015 is closed!
After the deadline we still have a limited number of places available for incomings from abroad and for master students coming from other universities and starting at TUM this summer. If this applies to you, please write an email to albrechtma.tum.de.

The registration is done by email to albrechtma.tum.de providing the following information:

**Registration for this course is mandatory and has to be done before the deadline: March 1, 2015.**The registration is done by email to albrechtma.tum.de providing the following information:

- last name, first name.
- curriculum (of your master's studies).
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects.

(Example: (1) Project 3 (2) Project 1 (2) Project 4 (3) Project 2 - note that you can rate multiple projects with the same value.) - list of optimization related lectures that you have attended (for lectures from other faculties or universities, please give a short description of the topics covered so that we know about your expertise in the field).
- programming skills (programming languages and other programming related skills).
- persons you would like to work with as a team.

# Preliminary Meeting

The preliminary meeting was on**January 28, 2015 at 16:30 in room MI 00.07.014**. At this meeting we presented some information about the case studies courses in general, what to expect during the courses, this year's projects, important dates and the registration process (see condensed version of the presentation slides).**Please note that a registration for this case study course is mandatory before the deadline on March 1, 2015!**If you have any questions that are not answered here or at the preliminary meeting, please contact Sebastian Albrecht.