Prof. Dr. Moritz Diehl - moritz.diehl@imtek.uni-freiburg.de

The course’s aim is to give an introduction into numerical methods for the solution of optimization problems in science and engineering. It is intended for students from two faculties, mathematics and physics on the one hand, and engineering and computer science on the other hand. This semester, Numerical Optimization is offered as an semi-online course. The focus is on continuous nonlinear optimization in finite dimensions, covering both convex and nonconvex problems.

The exam is March 4th at 9am in HS-00-036, G.-Köhler-Allee 101.

Organization of the course

The course during is based on two pillars, lectures and exercises, accompanied by written material for self-study. As the course is semi-online there will be no lecture held. Instead you can refer to the lectures recorded during the winter term 2015/16. Nonetheless we will meet every Friday, 14:00 to 16:00, in SR 226, Hermann-Herder-Str. 10 (Rechenzentrum). Usually every second Friday is dedicated to Q&A regarding the lecture. Normally both professor and teaching assistant will attend the Q&A session. Every other Friday there will be exercise sessions with the teaching assistant. There is a detailed calendar below. Course language is English and all communication is made via the course homepage. For more information please contact Florian Messerer.

For the lecture recordings please refer to the course page of winter term 2015/16.

This course gives 6 ECTS. It is possible to do a project to get an additional 3 ECTS, i.e. a total of 9 ECTS for course+project.

Exercises: The exercises are partially paper based and partially on the computer. Individual laptops with MATLAB installed are required. Please note that the reserved room is not a computer pool. The exercises will be distributed beforehand. You can then prepare yourselves for the exercise session, where you can complete the tasks in teams of 2 and show the results to the teaching assistant. Groups that require more time or cannot make it to the exercise session may send their solutions by e-mail (messerer@tf.uni-freiburg.de, see guidelines below) until the start of the next Q&A session. Note that groups that complete the tasks during the exercise session do not need to send a report by e-mail. You will need at least 40% of the total points in order to be eligible for the exam.

Final evaluation: For engineering students the final grade of the course (6 ECTS) is based solely on a final written exam at the end of the semester. Students from the faculty of mathematics need to pass the written exam (ungraded) in order take an oral exam, which determines their grade. The final exam is a closed book exam. Only pencil, paper, a calculator and two A4 sheets (4 pages) of self-chosen formulas are allowed (handwritten).

Projects: The project (3 ECTS) consists in the formulation and implementation of a self-chosen optimization problem and numerical solution method, resulting in documented computer code, a project report, and a public presentation. Project work starts in the last third of the semester and participants can work either individually or in groups of two people.

Calendar

Guidelines for handing in exercises

If you hand in the exercise via e-mail, please adhere to the following guidelines:

• One (!) file which is your main document (preferably pdf). It contains your name(s), your solutions to the pen-and-paper exercises and for computer exercises the name of the corresponding file(s).
• The main document can be a scan of your handwritten solutions or created with a text editor of your choice (with proper support for mathematical notation, e.g. Latex, MS Word, Open Office...)
• Hand in all of the relevant code files. It should be possible to run them to see all results. It should not be necessary to un(comment) lines for proper functioning. If there are several similar, but conflicting versions (e.g. different constraints), please hand them in as separate files.
• If you received helper functions as part of the exercise, please also hand them in. This makes it easier to run your files since everything is contained in one folder already.

Project

Please find the guidelines for the 3ECTS project here.

The final presentation will be a talk of 10 minutes plus up to 10 minutes of questions. Please try to stick to the 10 minutes as close as possible.

We have the following 4 topics: The Dogleg Method, The Generalized Gauss-Newton Method, Optimal Control of Table Soccer, Optimization of a Hammer Throw, Optimal Control of Apollo Re-entry

The schedule for Friday, Feb 8th is as follows:

Material

• lecture recordings
• lecture notes
• past exam
• Jorge Nocedal and Stephen J. Wright, Numerical Optimization, Springer, 2006.
• Amir Beck, Introduction to Nonlinear Optimization, MOS-SIAM Optimization, 2014.
• Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge Univ. Press, 2004.

Miscellaneous

• You can watch the lecture recordings together. We reserved SR 226, Hermann-Herder-Str. 10, every Friday 4 to 8 pm. This is completely self organized, so neither Prof. Diehl nor the teaching assistant will attend. You just need someone to bring a laptop (and maybe portable speakers). There's a VGA cable and a HDMI port without cable.