Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Optimization II
SoSe 2022

Luise Blank

Type of course (Veranstaltungsart)

German title
Optimierung II

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.

  • 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

Mo, We 10-12, Exercise class presumably Th12-14

Mo M101, We M104, Th M104

  • 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,
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

9, für RZ M 04, RZ-M61, RZ-M33: 6