Optimization I

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Optimization I

Semester
WiSe 2024 / 25

Lecturer
Luise Blank

Type of course (Veranstaltungsart)
Vorlesung

German title
Optimierung I

Contents
Multiple Applications lead to continuous optimization problems, such as calculating the optimal path for robotic arms and for flight trajectories, identifying the seismological properties of the earth, developing investment portfolios, controlling chemical processes, and surface optimization in the automotive industry. This lecture addresses the theory and numerics of continuous optimization.
After a brief introduction to various optimization tasks, we first discuss nonlinear minimization without constraints. The two fundamental numerical strategies, line search and trust-region methods, are covered.
Next, the theory of optimization under constraints is derived, including constraint qualifications, optimality conditions and Lagrange multipliers. Finally, we introduce and analyze for linearly constraint optimization problems with quadratic cost function the active-set strategy.
In the following semester the theory and numerics will be extended to nonlinear problems with constraints.
As programming language we use Matlab which is introduced in the exercise classes.

Literature

J. Nocedal, S.J. Wright: Numerical Optimization, Springer-Verlag.

Chr. Grossmann, J. Terno: Numerik der Optimierung, Teuber-Studienbücher.

C. Geiger, C. Kanzow: Numerische Verfahren zur Lösung unrestringierter Optimierungsaufgaben, Springer.

C. Geiger, C. Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben, Springer.

W. Alt: Nichtlineare Optimierung, Eine Einführung in Theorie, Verfahren und Anwendungen, Vieweg Verlag.

R. Fletcher: Practical Methods of Optimization, John Wiley & Sons.

I. Griva, S.G. Nash, A. Sofer: Linear and Nonlinear Optimization, SIAM.

Recommended previous knowledge
Lineare Algebra, Analysis, Numerik I

Time/Date
Mo 14-16, We 10-12, Exercise class presumably Tue 10-12, Wed 14-16

Location
Mo: M103, We: M103, exercise class M102/PHY 5.0.20

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=67031
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Preliminary registration for the organisation of exercise classes: at the end of the previous
semester via EXA or LSF (see announcement by the department)
Registration for the exercise classes: under GRIPS
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of the points of the theoretical as well
as of the programming exercises. The exercises for the IT-Ausbildung will be indicated.

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 min., Date: by arrangement, re-exam: Date: by arrangement

Modules
BPraMa(2), BV, MV, MAngAn, CS-B-Math3, CS-B-P16, PHY-B-WE 03, PHY-M-VE 03, RZ M 04, RZ-M61, RZ-M33

ECTS
9, für RZ M 04, RZ-M61, RZ-M33: 6

Druckansicht