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Technische Universität München, Zentrum Mathematik

Case Studies in Nonlinear Optimization

Combined Lecture and Project Work Course

Sebastian Albrecht and Christian Böhm

Summer Term 2014

News - Basic Concept- Projects- Materials - Schedule- Registration


Jun. 24 The final workshop is on July 5 (see conference webpage for details).

Apr. 28 Keep the poster deadline on May 4 in mind!
Apr. 28 Valid computer accounts (indentical to the ones needed for the Rechnerhalle) are needed for the computer room. If you have no account or forgotten your passwort, please contact the infopoint before the lectures start!
Apr. 28 Lectures on Wednesday 30.4. and Monday 05.05. take place in the computer room MI 00.07.037. Feel free to bring your laptop along.
Apr. 16 Program code for IPOPT and Casadi (plus Deal.ii for some teams) added to repositories. Slides for programming exercises (within the case study units of the next weeks) added to website.
Apr. 8 Added section with download materials: see here.
Mar. 27 Time-slot of lectures on Wednesdays changed to 2pm - 4pm. See schedule for details.
Feb. 7: Lectures will be on Mondays and Wednesdays. See schedule for details.
Feb. 3 Five potential topics for the projects published; cf. projects.
Jan. 20 There will be a preliminary meeting for this course on February 7, 12:15 pm in room MI 00.09.022. See schedule for details.
Jan. 20 The number of participants is strictly limited. Registration by email to albrechtematma.tum.de no later than March 1. See registration for details.

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.


Next Generation Traffic Control
In a few years cars will be sold which exchange information with other cars or hardware like traffic lights. The goal of this project is to use, for example, the positional information of the cars to optimize the control of traffic lights according to the current traffic situation. Methods of real-time optimization are needed for sufficiently fast reactions to changes of traffic situations.

Airplane Control in Turbulences
Wind influences airplane control critically, but changes of wind can hardly be predicted. Consequently, a beforehand optimized control strategy is of limited value and the optimal control problem has to be solved repeatedly during the flight. Therefore the goal of this project is to realize a model predictive control strategy which adapts to external influences.

Optimally Adapting Crane Control
Huge warehouses are needed to cope with the boom of online shopping and new systems are needed to efficiently store and retrieve the items in the high-racks. The advantage of traveling cranes over common forklift trucks is their flexibility and the possibility to use more than one crane for each high-rack. However, different loads result in different dynamics of the crane system and thus the goal of this project is to determine the physical properties of the loads in an optimal manner while handling them.

Calibration of Financial Market Models
Financial market models are employed to determine the fair value of derivatives and options. These models usually depend on several parameters that have to be estimated based on available market data before the model can be applied for pricing or hedging purposes. This process is called "calibration of the model" and typically involves solving a nonlinear least squares problem subject to model dependent constraints. Efficient optimization methods are required since shifts on the stock market require frequent recalibrations of the models.

Optimal Design of Experiments in Geophysical Exploration
The search for natural resources (e.g., gas or oil) requires knowledge of the Earth's subsurface. Seismic tomography is an imaging technique to determine the material structure and can be used to reveal the Earth's interior. For the collection of data, seismic waves are excited by small explosions in boreholes or agitations at the surface. Afterwards, the "seismic response" of reflected and refracted waves is recorded by an array of seismometers. This process is costly and therefore strategies are needed to design these experiments in an optimal manner.


Preliminary Meeting:

A preliminary meeting will take place on February 7th, 2014, 12:15 pm in room MI 00.09.022. At this meeting, we will give you 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. This is a joint meeting for both the "Case Studies Discrete Optimization" and the "Case Studies Nonlinear Optimization". If you cannot come to this meeting but would still like to participate in the course, some more information will be published after the meeting. Please note that registration by March 1st, 2014 is mandatory! If you have any questions that are not answered here or at the preliminary meeting, please contact Sebastian Albrecht.

Here is a shortened version of the slides used for the preliminary meeting (in German).

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 will be on Monday, April 7th!
On Wednesday June 04 the midterm presentations take place between 14:00 and 16:00 (2 hours).

Mondays 10:15 - 11:45 MI 00.07.014
Wednesdays 14:00 - 15:30 MI 00.07.014


Mandatory Elements:
Please make sure to reserve the following two dates (attendance is absolutely mandatory) in addition to the two time-slots mentioned above: The final workshop is the last official date for the course.


Slides, Handouts and additional materials will be available here shortly after the lectures.
Note that a user name and a password is needed to access them (contact your team advisor if you do not have this information).

Kickoff slides
Project Planning slides (incl. introduction to TortoiseHg Pfeil and Trac Pfeil)
Poster Design organization slides, design slides, presentation slides
Case Study: Modeling robot example modeling slides
Case Study: IPM IPM slides, AD slides
Case Study: Software robot example computation slides
Case Study: Visualization robot example visualization slides
Introduction to deal.ii slides


Registration for the case studies in nonlinear optimization 2014 is closed!

Knowledge of the content of (basic) courses on unconstrained and constrained optimization (e.g., courses MA2503 (Nichtlineare Optimierung: Grundlagen) and MA3503 (Nonlinear Optimization: Advanced)) is mandatory. Further courses on nonlinear optimization are not required, but may be helpful.
Participation in the computer course on nonlinear optimization is strongly recommended. This course will take place between winter term and summer term 2014 and further information will be published here when available.

Registration for this course is mandatory and the registration deadline is March 1st, 2014!
The registration is done by email to albrechtematma.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.
  • 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.
After March 1st, 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 albrechtematma.tum.de.