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Courses
WS 2006/07:
- Numerical Mathematics (6.016 + 6.018)
- Lectures: Peter Brucker
in 31/E06 at Monday 14-16 and Friday 14-16
- Exercise Sessions: Christian Strotmann
- in 31/E06 at Thueday 14-16
- Basic methods of numerical mathematics are presented. Especially methods
for solving linear and nonlinear systems of equations, interpolation problems,
ordinary and partial differential equations are discussed.
In the exercise sessions both theoretical questions are treated and practical
problems are solved with computer programming.
Prerequisites:
Linear Algebra
Literature:
H.R. Schwarz, Numerische Mathematik, Teubner, Stuttgart, 1988.
- Optimization (6.134 + 6.136)
- Lectures: Peter Brucker
in 31/E06 at Wednesday 10-12 und in 31/E06 at Friday 10-12
- Exercise Sessions: Christian Strotmann
- in 31/E06 at Monday 10-12
- Discrete optimization problems shortest path and network flow problems, knapsack problems,
travelling salesman problems, routing problems, scheduling problems, etc. are
introduced and the complexity of these problems will be investigated. Methods
and tools to solve these problems like linear programming, dynamic programming,
local search, genetic algorithms,
branch-and-bound methods, neural networks will be discussed. The concept will be
applied to different types of machine scheduling problems.
Prerequisites:
Linear algebra, Algorithms and data structures
Literature:
P. Brucker and S. Knust, Complex Scheduling, Springer, Heidelberg, 2006.
SS 2006:
- Scheduling (6.172)
- Lectures: Peter Brucker
in 69/E23 at Wednesday 12-14 und in 69/E23 at Friday 12-14
- Scheduling theory deals with the temporary planning of activities with limited ressources.
Depending on the specific problem the activities are jobs, tasks,
lectures, trains, etc. The corresponding ressources are for instance machines, processors,
teachers, parts of tracks, etc. The corresponding problems are machine or
computer scheduling problems, school or railway time-tabling, etc.
For solving general and specific
scheduling problems suitable methods are developed.
Prerequisites:
Linear algebra, Algorithms and data structures
Literature:
P. Brucker and S. Knust, Complex Scheduling, Springer, Heidelberg, 2006.
WS 2005/06:
- Optimization (6.134 + 6.136)
- Lectures: Peter Brucker
in 69/117 at Tuesday 08-10 und in 31/E06 at Friday 12-14
- Exercise Sessions: Thomas Kampmeyer
- in 69/117 at Thursday 10-12
-
The main topic of this course is an introduction to linear programming. It covers basic theory,
selected applications, network flow problems, and advanced techniques. Beside methods for
efficient implementations of the simplex method various ways in which linear programming
can be applied to practical concerns are presented. The practical application cover
production scheduling, the cutting stock problem, network flows, machine scheduling, and
project planning. Linear programming is the basis for advanced topics in optimization like
nonlinear optimization and combinatorial optimization
WS 2004/05:
SS 2004:
WS 2003/04:
SS 2003:
- Linear Optimization ()
- Lectures: Peter Brucker
- in at and
- Exercise Sessions: Christian Strotmann
- in at
- The main topic of this course is an introduction to linear programming. It covers basic theory, selected applications, network flow problems, and advanced techniques.
Beside methods for efficient implementations of the simplex method various ways in which linear programming can be applied to practical concerns are presented. The practical application cover production scheduling, the cutting stock problem, network flows, machine scheduling, and project planning. Linear programming is the basis for advanced topics in optimization like nonlinear optimization and combinatorial optimization.
Prerequisites:
Knowledge of numerical methods for solving systems of linear equations.
Literature:
V. Chvatal, Linear Programming, W.H. Freeman and Company, New York,
1983.
- Introduction to discrete Optimization ()
- Lectures: Peter Brucker
in at und in at
- Discrete optimization problems like graph coloring problems, knapsack problems,
travelling salesman problems, routing problems, scheduling problems, etc. are
introduced and the complexity of these problems will be investigated. Methods
and tools to solve these problems like local search, genetic algorithms,
branch-and-bound methods, neural networks will be discussed. The concept will be
applied to different types of machine scheduling problems.
Prerequisites:
Linear Programming, Algorithms and data structures
Literature:
P. Brucker, Scheduling Algorithms, Springer, Berlin, 1995, 1998, 2001.
WS 2002/03:
- Numerical Mathematics (6.016 + 6.018)
- Lectures: Peter Brucker
in 31/E06 at Mon 12-14 and Wed 12-14
- Exercise Sessions: Silvia Heitmann
- in 31/E05 at Fri 8-10
- Attention: The beginning of the lectures postpones to Wednesday, 16.10.2002,
at 12.15 in room 31/E06 !!
- Basic methods of numerical mathematics are presented. Especially methods
for solving linear and nonlinear systems of equations, interpolation problems,
Fourier-approximation and the fast Fourier-Transformation are discussed.
In the exercise sessions both theoretical questions are treated and practical
problems are solved with computer programming.
Prerequisites:
Linear Algebra
Literature:
H.R. Schwarz, Numerische Mathematik, Teubner, Stuttgart, 1988.
- Network Flows (Graph-algorithms) (6.138)
- Lectures: Peter Brucker
- in 31/449a at Mon 8-10 and Wed 8-10
- Attention: The beginning of the lectures postpones to Wednesday, 16.10.2002,
at 8.30 in room 31/449a !!
- Algorithms for solving shortest path, maximum flow, and minimum cost flow
problems are presented. Also generalizations of the minimum cost flow problem
like convex cost flow, generalized flow, and multi-commodity flow problems
are discussed. The algorithms are based on linear programming, efficient data
structures, scaling techniques, and Lagrangian relaxation. Applications of
network flows to a variety of engineering, management, and other scientific domains
are given.
Prerequisites:
Basic knowledge on data structures and algorithms
Literature:
R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows, Prentice Hall, Upper Saddle
River, New Jersey, 1993.
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