Topics

The course covers theory and methods for nonsmooth optimization problems and nonsmooth systems of equations. Nonsmooth structures appear frequently in optimization and often allow to reformulate inequalities equivalently through equations or penalty terms. Nonsmooth regularizers are also highly relevant in data science, mathematical imaging, and related fields since they promote desired features such as sparsity. In class, nonsmooth analysis and selected methods for nonsmooth optimization are discussed. Moreover, examples and applications are provided.

The syllabus is found here.

News

October 8, 2018	You can review your exam of October 8, 2018 next Tuesday (October 16, 2018) from 3:30 p.m. until 4 p.m. in room 03.08.061. Please bring your student ID and a photo ID (e.g. passport). Further information can be found below. If you have any questions, feel free to contact Johannes Milz.
August 9, 2018	You can review your exam on Monday (August 13, 2018) from 11:30 a.m. to noon in room 3.8.22A. Please bring your student ID and a photo ID (e.g. passport). Further information can be found below. If you have any questions, feel free to contact Johannes Milz.
June 20, 2018	We won't be offering tutorials in the first week of July. The next tutorials are in the final week of the lecture period. Times and rooms are indicated below.
June 6, 2018	Information about the exams has been published (see below).
June 6, 2018	Classes already start at 2 p.m. and end at the usual time.
April 17, 2018	The course "Nonsmooth Optimization [MA5510]" can be used to substitute "Modern Methods in Nonlinear Optimization [MA 4503]." Meaning, if you pass the final exam of the course "Nonsmooth Optimization [MA5510]" you can request that your transcript indicates that you have passed "Modern Methods in Nonlinear Optimization [MA 4503]." You can request [MA5510] to count as [MA 4503] by sending an e-mail to master@ma.tum.de. Please provide your student ID number in that e-mail.
April 11, 2018	We have provided details on tutorial sessions (see below). You can sign up for a tutorial group tonight at 7 p.m.
April 9, 2018	The first problem sheet has been uploaded. Dates for tutorial sessions will be announced soon.
March 16, 2018	The first class is held on April 17, 2018. The tutorials start in the second week of the semester as well.

Dates

Lectures
	Tuesday	2 p.m.-3:45 p.m.	00.09.022	Prof. Dr. Michael Ulbrich

Tutorials
Group 2	Monday	14:15 - 15:45	Room	Johannes Milz	next session: Date
Group 1	Wednesday	12:15 - 13:45	Room	Johannes Milz	next session: Date

The final dates for the tutorials are available here.
We offer two tutorial groups. Please sign up for one of them.
The tutorials start in the second week of the semester. The next tutorials are held in the third week of the semester and then every other week, i.e. in the fifth, seventh, etc. week of the semester. This is because of limited availability of class rooms and allows for convenient times for the tutorial sessions. Moreover, that way you can attend tutorials on Exercises for Modern Methods in Nonlinear Optimization [MA4503] as well.

Exams

Schedule

The exam dates, times and places posted below are preliminary and are subject to change. Please consult TUMonline for the official dates.

First exam	July 31, 2018	3 p.m. - 4 p.m.	MI HS 2
Second exam	October 8, 2018	10 a.m. - 11 a.m.	MI HS 3

Important information about the first exam:

Registration via TUMonline is mandatory for participation in the exam (registration for the lecture and/or the tutorial classes does not suffice)! Registration for the first exam has started on May 15, 2018 and ends on June 30, 2018. Please be sure to register till then - you will not be allowed to take the exam without prior registration on TUMonline.
In case you have been granted any special regulations for your examination, please make sure to inform Johannes Milz right after registration and not later than July 15, 2018. Failure to notify us by that time implies you voluntarily forfeit your right to any special regulations for the exam.
The dates, times and places regarding the exam and the registration, which are posted above, are preliminary and subject to change. Please consult TUMonline for the official dates.

The exam will be comprehensive. All topics dicussed in class, in the tutorial and on the problem sheets are relevant for the exam.
The exams will be closed book. Meaning you are not allowed to use any lecture notes and cheat sheets during the exam.

The exam takes 60 minutes. In addition, before the beginning of the examination, each student will be given five minutes to read through the exam. In this period, writing is not allowed.
Be sure to bring a photo ID (passport or identity card) and your student ID. We will check the IDs during the exam.
On doors of the examination room, a list of student ID numbers assigning a seat to each student. Please find your student ID number and locate the correct seat in the examination room. Please do not store your belongings in rows in front of or behind your assigned seat.
Be sure to switch off any mobile phones, calculators, tablet computers, smart watches and other electronic devices and store them out of sight, e.g. in your bag. Handling and using any kind of electronic devices, whether switched on or not, will be considered an attempt to cheat.
Please do not use red or green pens nor a pencil.

Inspection for the first exam (Klausureinsicht):

Date and time for the inspection will be announced soon.
Be sure to bring a photo ID (the student ID is not sufficient).
If you cannot come yourself, you can authorize a representative to inspect your exam for you and (if necessary) demand a revision of the grading on your behalf. To do so, please issue a written authorization, which explicitly states your name and date of birth and the name and date of birth of the authorized person, and sign it. The authorized person will have to present a photo ID.
Applications for revised grading (Zweitkorrektur) are only possible during the inspection.

Information about the second exam:

Registration via TUMonline is mandatory for participation in the exam (registration for the lecture and/or the tutorial classes does not suffice)! Registration for the second exam starts on September 10, 2018 and ends on September 24, 2018. Please be sure to register till then - you will not be allowed to take the exam without prior registration on TUMonline.
In case you have been granted any special regulations for your examination, please make sure to inform Johannes Milz right after registration and not later than September 28, 2018. Failure to notify us by that time implies you voluntarily forfeit your right to any special regulations for the exam.
The dates, times and places regarding the exam and the registration, which are posted above, are preliminary and subject to change. Please consult TUMonline for the official dates.

The same terms and conditions as for the first exam apply to the second exam as well, which are found above.

Inspection for the second exam (Klausureinsicht):

Date and time for the inspection will be announced soon.
Be sure to bring a photo ID (the student ID is not sufficient).
If you cannot come yourself, you can authorize a representative to inspect your exam for you and (if necessary) demand a revision of the grading on your behalf. To do do, please issue a written authorization, which explicitly states your name and date of birth and the name and date of birth of the authorized person, and sign it. The authorized person will have to present a photo ID.
Applications for revised grading (Zweitkorrektur) are only possible during the inspection.

Lecture Notes

During the semester, lecture notes will be posted on moodle.

Tutorials and Problem Sheets

Graduate Teaching Assistant for the class is Johannes Milz. He is responsible for the tutorials and problem sheets. If you have any questions, feel free to contact Johannes Milz.
We post solutions for all problems which are not discussed in the tutorials on moodle. You will need a TUM-ID to login to moodle. Please note, that you need to register for a tutorial class to get access to solution sheets. If you experience any issues with accessing moodle, please contact Johannes Milz.

Literature

Geiger, Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben, Springer, 2002.
Alt: Numerische Verfahren der konvexen, nichtglatten Optimierung, Teubner, 2004.
Clarke: Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
Parikh, Boyd: Proximal Methods, Foundations and Trends in Optimization Vol. 1, No. 3, pp. 123–239, 2014.