35448 - Optimization Methods Modulübersicht

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
  1. Introduction. Optimisation problem formulation. Classification of problems. The standard form of an optimisation problem. Objective function and optimisation variables. Examples.
  2. Mathematical preliminaries. Vectors and Matrices. Elements of differential calculus. Convex sets and functions.
  3. Unconstrained problems. Optimality conditions for unconstrained problems.
  4. Unconstrained minimization techniques. The steepest descent method. Conjugate gradient. The Newton methods.
  5. One-dimensional search methods. Golden section search.
  6. Nonlinear constrained optimisation. Kuhn-Tucker conditions. Lagrangian function. Lagrangian duality.
  7. Penalty methods. Linear programming. The simplex method. Integer optimisation.
  8. Genetic algorithms. Neural networks. Interior-point methods.
  9. Numerical matrix operations. Numerical solutions to rule-based optimization problems.
Excercises
  1. Optimisation problem formulation, mathematical models of problems.
  2. Analytical minimization techniques.
  3. Numerical methods: the steepest descent, conjugate gradient, the Newton methods.
  4. Linear programming.
  5. The application of Matlab Optimization Toolbox.
The students use available Matlab procedures and toolboxes
Recommended Prerequisites:Knowledges:
  • Basics in mathematics
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:
  • no assignment
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:
  • no assignment