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: TBA

Course Information

Attention: The lecture on Tuesday 2024-10-22 has been cancelled.

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 summer break. You can register for the exam via heiCO(1100122500, 1100122501), as soon as an exam is listed there The registration and cancellation cut-off dates listed in HeiCo apply.

Exam Format

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

Exam Dates

The exam dates and times will be listed here asap. We will open booking of timeslots asap as well and notify the class via MÜSLI with more information on the process.

Course Material

Lecture Notes

Exercises

Literature

TBA