65-441 Optimization of Complex Systems (in Englisch) (Blockveranstaltung in den letzten 7 Wochen der Vorlesungszeit)

Lehrende: Prof. Dr. Juan Carlos De los Reyes

Veranstaltungsart: Vorlesung

Anzeige im Stundenplan: M-VMMOA-V

Semesterwochenstunden: 2

Unterrichtssprache: Englisch

Min. | Max. Teilnehmerzahl: 5 | -

Kommentare/ Inhalte:
This lecture will emphasize on large-scale nonlinear optimization methods. Unconstrained and box-constrained problems will be considered and optimality conditions derived. Numerical methods for the solution of such problems will be studied in depth.

The aim of this lecture is to introduce the main ideas of numerical optimization methods for nonlinear problems.

The content of the lecture includes:
-First and second order optimality conditions
-Descent methods and line search strategies
-Newton and Newton-type methods
-Quasi Newton methods
-Trust region methods
-Projection methods
-Semi smooth Newton methods


Office hours: Thu 16:00-17:00, or by appointment

Literatur:
The content of this lecture is not summarized in one particular book, but either of the following will cover most of the content:

Kelley: Iterative methods for optimization
Nocedal, Wright: Numerical Optimization
Ulbrich, Ulbrich: Nichtlineare Optimierung

For additional reading the following books may be of interest:
Hinze, Pinnau, Ulbrich, Ulbrich: Optimization with PDE constraints
Luenberger: Optimization by vector space methods
Ito, Kunisch: Lagrange Multiplier Approach to Variational Problems and Applications

Modulkürzel:
Ma-M-VMMOA_n

Zusätzliche Hinweise zu Prüfungen:
Homework:

* There will be homework sheet to be solved available electronically.
* All exercises may be solved in teams of at most three people.

Exam:

* At the end of the term there is an examn, which has to be passed to get a certificate.
   Condition for participation are:
       -At least 50% of the homework credit points have been reached.
       -Active participation in the exercise class.
 
* Date and time of the exam are shortly after the end of the semester. The exact date is to be announced.
* Certificates have a grade, according to the grade reached in the exam.

Criteria for the certificate:

* Active contribution in the exercise class
* 50 % of the total number of homework points
* Exam successfully passed