This entry is from Summer semester 2021 and might be obsolete. No current equivalent could be found.

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

 Level, degree of commitment Specialization module, depends on importing study program 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): 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 the degree program M.Sc. Mathematics. Subject, Origin Mathematics, 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

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.