Technische Universität München, Zentrum Mathematik

Case Studies in Nonlinear Optimization

Combined Lecture and Project Work Course

Dr. Sebastian Albrecht

Summer Term 2015

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Basic Concept- Projects - Schedule - Registration/Preliminary Meeting

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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

Please see Moodle for further information on the lectures, organization and your team material. Search for the course "Fallstudien: Nichtlineare Optimierung" and sign in with your password.

Registration

Registration for the case studies in nonlinear optimization 2015 is closed!