Module Number:
| 35448
- module is no longer offered from WS 2011/12 |
Module Title: | Optimization Methods |
|
Optimierungsmethoden
|
Department: |
Faculty 3 - Mechanical Engineering, Electrical Engineering and Industrial Engineering
|
Responsible Staff Member: | -
Prof. Dr.-Ing. Schwarz, Harald
|
Language of Teaching / Examination: | English |
Duration: | 1 semester |
Frequency of Offer: |
Every summer semester
|
Credits: |
4
|
Learning Outcome: | Students will learn foundations of optimization methods and their numerical application in engineering. The students will be skilled to optimize various types of practical industrial problems |
Contents: | Lecture
- Introduction. Optimisation problem formulation. Classification of problems. The standard form of an optimisation problem. Objective function and optimisation variables. Examples.
- Mathematical preliminaries. Vectors and Matrices. Elements of differential calculus. Convex sets and functions.
- Unconstrained problems. Optimality conditions for unconstrained problems.
- Unconstrained minimization techniques. The steepest descent method. Conjugate gradient. The Newton methods.
- One-dimensional search methods. Golden section search.
- Nonlinear constrained optimisation. Kuhn-Tucker conditions. Lagrangian function. Lagrangian duality.
- Penalty methods. Linear programming. The simplex method. Integer optimisation.
- Genetic algorithms. Neural networks. Interior-point methods.
- Numerical matrix operations. Numerical solutions to rule-based optimization problems.
Excercises
- Optimisation problem formulation, mathematical models of problems.
- Analytical minimization techniques.
- Numerical methods: the steepest descent, conjugate gradient, the Newton methods.
- Linear programming.
- The application of Matlab Optimization Toolbox.
The students use available Matlab procedures and toolboxes |
Recommended Prerequisites: | Knowledges:
|
Mandatory Prerequisites: | None |
Forms of Teaching and Proportion: | -
Lecture
/ 2 Hours per Week per Semester
-
Exercise
/ 1 Hours per Week per Semester
-
Self organised studies
/ 75 Hours
|
Teaching Materials and Literature: | - E.K.P. Chong, S.H. Zak: An Introduction to Optimization, 2nd edition, New York, John Wiley, 2001.
- J.F. Bonnans: Numerical optimization: theoretical and practical aspects, Springer-Verlag, 2003.
- M. Asghar Bhatti: Practical Optimization Methods, Berlin, Springer-Verlag 2000.
|
Module Examination: | Unspecified - Specification from winter semester 2016/17 required! |
Assessment Mode for Module Examination: | - Written examination, 90 min
or
- verbal examination, 30 min
|
Evaluation of Module Examination: | Performance Verification – graded |
Limited Number of Participants: | None |
Part of the Study Programme: | |
Remarks: | The lecture will be offered by Dr. Janik and Dr. Leonowicz as blocks |
Module Components: | Optimazation Methods (lecture/exercise) |
Components to be offered in the Current Semester: | |