Voraussetzungen

Inhalte

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

Lernziele

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

Prüfungsleistung

• Written examination, 90 min or • verbal examination, 30 min

Literatur (3)

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.

Bemerkungen

The lecture will be offered by Dr. Janik and Dr. Leonowicz as blocks