Optimization II

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Optimization II

Semester
SoSe 2025

Lecturer
Luise Blank

Type of course (Veranstaltungsart)
Vorlesung

German title
Optimierung II

Contents
Building on the lecture Optimization I, this lecture deals with numerical methods for nonlinear, restricted optimization problems. First, methods for linear restricted problems and convex optimization problems are considered. The theory of restricted problems is complemented by duality concepts and saddle point statements for the Lagrangian function. Then, penalty, barrier and augmented Lagrangian function methods are analyzed for NLPs. The introduced concepts for QPs are extended to sequential quadratic programming and analyzed using techniques for Newton methods. We hereby obtain local convergence statements. For globalization, methods such as merit functions and filtering procedures are introduced. For a modified, globalized SQP procedure, global convergence is analyzed.

Literature

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

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

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

F. Jarre und J. Stoer: Optimierung, Springer-Verlag.

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
Optimization I

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

Location
Mo M103, We M103, Exercise: We M104

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=69467
(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: via 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