This entry is from Winter semester 2018/19 and might be obsolete. No current equivalent could be found.

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

 Level, degree of commitment Specialization 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(s): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. Duration,frequency One semester, Im Wechsel mit anderen specialization 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die entweder in den Basismodulen Lineare Algebra I, Lineare Algebra II, Analysis I und Analysis II oder Grundlagen der linearen Algebra, Grundlagen der Analysis und Grundlagen der Höheren Mathematik vermittelt werden. Außerdem werden die Kompetenzen aus dem Modul Maß- und Integrationstheorie empfohlen. Darüber hinaus sind Kenntnisse der Funktionalanalysis von Vorteil.

## Applicability

The module can be attended at FB12 in study program(s)

• M.Sc. Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

The module can also be used in other study programs (export module).

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.