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Methods of Optimization

Type of study Follow-up Master
Language of instruction English
Code 470-4503/02
Abbreviation MO
Course title Methods of Optimization
Credits 6
Coordinating department Department of Applied Mathematics
Course coordinator doc. Ing. Petr Beremlijski, Ph.D.

Subject syllabus

Lectures:
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization methods for constrained minimization. Augmented Lagrangians
Duality in convex programming. Saddle points.
Non-smooth optimization, subgradients and optimality conditions.
Software.

Exercises:
Introduction to the MATLAB programming.
Implementation of the golden section and Fibonacci series methods.
Implemenation of the Newton-like methods.
Implementation of the gradient based method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the augmented Lagrangian metod.
Solution of selected engeneering problems using optimization software.

Literature

BERTSEKAS, Dimitri P. Nonlinear Programming. 3rd edition. Athena Scientific, 2016. ISBN 978-1886529052.

Advised literature

NOCEDAL, Jorge a Stephen WRIGHT. Numerical Optimization. 2nd edition. Springer, 2006. ISBN 978-0387303031.