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.

*******************

Summer semester retake exam:

• Date&Time: 17.8.2020, 1pm
• Location: Georges-Köhler-Allee 101, HS 00-036
• Time for writing: 2h
• Further details see "Final evaluation" below

*********************

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 Tuesday, 14:00 to 16:00, in HS II (02 033), Albertstraße 23b. Usually every second Tuesday is dedicated to Q&A regarding the lecture. Normally both professor and teaching assistant will attend the Q&A session. Every other Tuesday there will be exercise sessions with the teaching assistant. A detailed calendar will be added 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 work  on the exercises  and get  help and feedback  from  the teaching assistants. We may also discuss solutions of previous sheets if there is demand. Solutions to the exercise sheets have to be handed in via e-mail to florian.messerer@imtek.de until the start of the next Q&A session. You will also have to indicate which of the exercises you successfully finished. We will not examine every solution of every student. Note however that we will do extensive random probing. Indicating a task as solved when this is not true will result in 0 points for the whole sheet. Also note the guidelines for handing in which you can find below. You will need at least 40% of the total points to pass.

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 master in mathematics need to pass the written exam (ungraded) in order take a graded oral exam. The final exam is a closed book exam. Only pencil, paper, a calculator and two A4 sheets (4 pages) of self-chosen content are allowed (handwritten).

Projects: The project (3 ECTS) consists in the formulation and implementation of a self-chosen optimization problem or 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 in groups of two to three 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). At the top should be your names and an overview of which tasks you solved. If you have solved a task only partially, you can indicate so.  This is then followed by your solutions to the pen-and-paper exercises, and for computer exercises the name(s) of the corresponding file(s). Claiming tasks as solved when this is not true will result in 0 points for the whole sheet.
• 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. Do not copy each other's code. This will result in 0 points for the sheet for all participating parties!

Project

The project guidelines can be found here.

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.