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German original

PDE-constrained Optimization
(dt. Optimierung bei partiellen Differentialgleichungen)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
Im Wechsel mit anderen advanced moduleen zur Optimierung
Person in charge of the module's outline Prof. Dr. Thomas Surowiec

Contents

I. Optimization in Hilbert spaces and unilateral boundary value problems (existence of minimizers, variational inequalities, function spaces and elliptic differential operators, numerical solution methods)

II. Optimization of elliptic partial differential equations (existence theory, optimality conditions, derivation of the adjoint state equation and the role of the adjoint state, state constraints, applications and numerical solution methods)

III. Optimization of elliptic partial differential equations under uncertainties (Bochner spaces, risk neutral, risk averse and robust problem formulations, existence and optimality theory, numerical solution methods)


Qualification Goals

The students shall

  • learn the theory and numerical methods of optimization in the context of partial differential equations,
  • acquire the competence to explain and apply them,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Linear Algebra I and Linear Algebra II and Analysis I and Analysis II or Basic Linear Algebra and Basic Real Analysis and Basics of Advanced Mathematics, Measure and Integration Theory. In addition, knowledge of functional analysis is an advantage.


Recommended Reading

(not specified)



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.