Infinite-Dimensional Optimization

Semester: 2024 WS
Class type: Lecture
Languages: English
Teachers: Roland Herzog, Georg Müller
Contact: Send e-mail
Websites for this class: MÜSLI, heiCO(1100122500, 1100122501)
Exam Dates: See below

Course Information

Description

This class covers optimality criteria and optimization algorithms for (un-)constrained scalar optimization problems that are formulated for optimization parameters from infinite-dimensional linear spaces with a focus on convex optimization with applications in imaging and on optimal control problems with partial differential equations as constraints.

Prerequisites

Skills from Analysis I and II (MA1/ MA2), Lineare Algebra I (MA4) as well as basic optimization skills are highly recommended. “Nonlinear Optimization” (finite dimensional constrained optimization) is not a mandatory requirement but a reasonable foundation. Skills from functional analysis are also helpful.

Concept and Components

This class is comprised of:

  • Detailed lecture notes
  • 2x 2h lectures per week
  • Exercise sheets with corresponding answer sheets
  • Tutorials for co-working on exercise sheets
  • Exams following the end of the lecture period

Dates and Schedule

Please refer to the class’ schedule for an overview of days and content weeks. More detailed information on the lecture can be found in heiCO(1100122500, 1100122501). More detailed information on the exercise labs can be found in MÜSLI.

Exercises

Exercises will be centered around one exercise sheet per week containing both theoretical/analytical questions and numerical/implementation exercises. Default programming language – in the sense that it will be used in our answer sheets and we will be providing support for it – will be Python. Feel free to work with another programming laguage that is suitable for implementing the optimization algorithms if you are self sufficient working with it.

In the exercise tutorials (see MÜSLI), you will have the oportunity to work on the exercise sheets with your peers and with support from the tutor. You can get the most out of your time there if you show up having already taken a first look at the exercises and bringing your own questions and discussion topics to the meetings. Feel free to ask questions on the lecture notes or the lectures as well. The exercise tutorials are designed for easy access for questions to the tutor and the opportunity to make quick progress with the exercise sheets.

After the work phase of each exercise sheet has ended, we will post sample solutions. To evaluate your success on the exercise sheets, please compare your work with the answer sheets we will provide and, of course, feel free to talk to your tutor in the labs. You are not expected to turn in your work.

Class Registration

To register for this class, please register for an exercise group at MÜSLI. Please also register in case you are interested in participating in this class but not in the exercise tutorials. This will allow us to get an idea of class demand.

Attention(!): Registration for the class does not automatically include registration for an examination. More information on the exams can be found in the section exams.

Exams

We will be offering exams at the end of the semester and during the following semester break.

Exam Format

We will be offering oral exams of about 30 minutes duration. You are free to choose from German or English as the language of your choice.

Exam Registration and Cancellation

Cut-off dates listed in HeiCO apply for both registration and cancellations.

In order to register for an exam, you need to do the following:

  1. Register for the class and the exercises in heiCO(1100122500, 1100122501).
  2. Register for the exam in heiCO(1100122500, 1100122501).
  3. Once you have registered for the exam in HeiCo, send us an email with the following information:
    • First and Last Name
    • Date of Birth
    • Place of Birth
    • Immatrikulation Nr. (your 7-digit Matrikel-Nr. not your URZ ID)
    • Course of study
    • First and second choice of the exam time blocks in the following section. Please note that we will be filling the slots on a first-come-first-served basis and that you will be assigned to the earliest vacant slot in your chosen time block.

Once processed, you will receive a confirmation email. With your exact time slot.

To cancel your registration, the HeiCo cancellation deadline applies. Please cancel in HeiCo and send us an email .

Exam Dates

Below is a list of possible exam dates. We will be posting, which time blocks are fully booked with a small time delay.

  • 2025-02-04 13:00-16:00h (slots available)
  • 2025-02-06 09:00-12:00h (fully booked)
  • 2025-03-11 09:00-12:00h (fully booked)
  • 2025-03-12 09:00-12:00h (fully booked)
  • 2025-03-13 13:00-16:00h (fully booked)

Course Material

Lecture Notes

Exercises

Literature

TBA