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Optimization (and Multiscale) Methods

Description

Optimization is of fundamental importance in virtually all branches of science and technology. As a consequence, optimization methods find their applications in numerous fields, starting from, e.g., network flow and ranging over shape optimization in engineering to optimal control problems. This course provides an introduction into the most important methods and techniques in discrete and continuous optimization. We will present, analyze, implement, and test methods for discrete and continuous optimization. This will include optimality conditions, the handling of linear and non-linear constraints, and methods such as interior point methods for convex optimization, Newton's method, Trust-Region methods, and optimal control methods. Furthermore, we will consider fast and massively parallel iterative  solution methods such as multigrid and domain decomposition, which are needed for solving the arising large scale linear sub-problems. By combining both method classes, we will eventually derive efficient optimization and solution methods for large scale optimization and minimization problems.

REFERENCES
Numerical Optimisation; Nocedal, Jorge, Wright, Stephen; Series: Springer Series in Operations Research and Financial Engineering,  2nd ed., 2006, XXII, 664 p. 85 illus., www.springer.com/mathematics/book/978-0-387-30303-1
A Multigrid Tutorial; William L. Briggs, Van Emden Henson, and Steve F. McCormick; Second Edition, SIAM, 2000 (book home page), ISBN 0-89871-4621.
Multigrid Methods and Applications; Wolfgang Hackbusch; Springer, 1985.
An Introduction to Multigrid Methods; Pieter Wesseling; Corrected Reprint. Philadelphia: R.T. Edwards, Inc., 2004. ISBN 1-930217-08-0.
Matrix computations; Gene H. Golub and Charles F. Van Loan.
Domain Decomposition Methods; Toselli, Widlund
Trust-Region Methods; Conn Gould Toint.
Practical Methods of Optimisation; R. Fletcher.

People

 

Krause R.

Course director

Kopanicakova A.

Assistant

Pozzi S.

Assistant

Additional information

Semester
Spring
Academic year
2016-2017
ECTS
6
Education
Bachelor of Science in Informatics, Core course, Lecture, 3rd year

Master of Science in Computational Science, Core course, Lecture, 1st year

PhD programme of the Faculty of Informatics, Elective course, Lecture, 1st and 2nd year (4 ECTS)