Czech

Not applicable.

The course is designed for mathematical engineers and it is useful for applied sciences students. Students will learn the theoretical background of fundamental topics in optimization (especially linear and non-linear programming). They will also made familiar with useful algorithms and interesting applications.

Fundamental knowledge of principal concepts of Calculus and Linear Algebra in the scope of the mathematical engineering curriculum is assumed.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

The course contains lectures that explain basic principles, problems and methodology of the discipline, and exercises that promote the practical knowledge of the subject presented in the lectures.

Graded course-unit credit is awarded based on the result in a written exam involving modelling-related, computational-based, and theoretical questions. The short oral exam is also included.

1. Introductory optimization: problem formulation and analysis, model building, theory.
2. Visualisation, algorithms, software, postoptimization.
3. Linear programming (LP): Convex and polyhedral sets.
4. LP: Feasible sets and related theory.
5. LP: The simplex method.
6. LP: Duality, sensitivity and parametric analysis.
7. Network flows modelling.
8. Introduction to integer programming.
9. Nonlinear programming (NLP): Convex functions and their properties.
10. NLP: Unconstrained optimization and line search algorithms.
11. NLP: Unconstrained optimization and related multivariate methods.
12. NLP: Constrained optimization and KKT conditions.
13. NLP: Constrained optimization and related multivariate methods.
14. Selected general cases.

Not applicable.

The course objective is to emphasize optimization modelling together with solution methods. It involves problem analysis, model building, model description and transformation, and the choice of the algorithm. Introduced methods are based on the theory and illustrated by geometrical point of view.

The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.

Not applicable.

Not applicable.

Bazaraa et al.: Linear Programming and Network Flows, , Wiley 1990 (EN)
Bazaraa et al.: Nonlinear Programming, , Wiley 1993 (EN)
Dupačová et al.: Lineárne programovanie, Alfa 1990 (SK)

Dvořák a kol.: Operační analýza, , 2002 (CS)
Charamza a kol.: Modelovací systém GAMS, , 1995 (CS)
Klapka a kol.: Metody operačního výzkumu, , 2000 (CS)