Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-16-M-7

Optimization with PDE (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-16-M-7 Optimization with PDE 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-16-K-7
Optimization with PDE
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-16-K-7]: Title: "Optimization with PDE"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86350 ("Optimization with PDE")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Mathematical concepts dealing with optimization problems with differential equation constraints are provided and analysed. In particular, the following contents are covered:
  • non-linear theory of operators,
  • adjoint calculus,
  • approximation methods for numerically solving constrained optimization problems

Competencies / intended learning achievements

Upon successful completion of the module, the students are able to cope with the theory and numerical methods to analyse and solve constrained optimization problems. They can analyse the algorithms and apply them to concrete problems. Moreover, they can critically assess the possibilities and limitations of the use of these algorithms. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

With the help of concrete exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture.

Literature

  • M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich: Optimal Control of Partial Differential Equations,
  • F. Troeltzsch: Optimale Steuerung partieller Differentialgleichungen,
  • J.L. Lions: Optimal Control of Systems Governed by Partial Differential Equations,
  • D.G. Luenberger: Optimization by Vector Space Methods.

Requirements for attendance (informal)

Knowledge from the module [MAT-81-11-M-7] is useful, but not necessarily required.

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-81-16-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)