Skip to main content
Skip header
Close

Searching

Optimization Methods

Type of study Follow-up Master
Language of instruction Czech
Code 157-0372/02
Abbreviation OM
Course title Optimization Methods
Credits 5
Coordinating department Department of Systems Engineering and Informatics
Course coordinator prof. Mgr. Ing. František Zapletal, Ph.D.

Subject syllabus

1. Linear programming (model, solution, duality).
2. Necessary and sufficient conditions of optima (KKT conditions), Trap of local optima).
3. Risk - random variables and its description.
4. Stochastic programming - introduction, classification.
5. Stochastic programming - single-stage models, chance constraints.
6. Stochastic programming - two-stage models (models with recourse), multi-stage models.
7. Stochastic programming - mean-risk portfolio models.
8. Introduction to fuzzy sets, logic and algebra.
9. Fuzzy programming - selected defuzzification measures, alpha-cuts, possibilistic programming.
10. Fuzzy programming - flexible programming models.
11. Data Envelopment Analysis (DEA) - introduction.
12. Data Envelopment Analysis (DEA) - CCR and BCC model.

Literature

SHAPIRO, Alexander, RUSZCZYNSKI, Andrzej a Darinka DENTCHEVA. Lectures on Stochastic Programming: Modeling and Theory, 2009. ISBN 978-0-89871-687-0 .
FIEDLER, Miroslav a kol. Linear optimization problems with inexact data. New York: Springer, 2006. ISBN 0-387-32697-9.
PRÉKOPA, András. Stochastic programming. Dordrecht: Kluwer Academic Publishers, c1995. Mathematics and its applications, v. 324. ISBN 0-7923-3482-5.

Advised literature

TAHA, Hamdy A. Operations research: an introduction. 9. vyd. International ed. Upper Saddle River: Pearson, 2011. ISBN 978-0-13-139199-4.
SHAPIRO, Alexander a Andrzej RUSZCZYŃSKI, ed. Stochastic programming. Amsterdam: Elsevier, 2003. Handbooks in operations research and management science, v. 10. ISBN 0-444-50854-6 .
VLACH, Milan a Jaroslav RAMÍK. Generalized concavity in fuzzy optimization and decision analysis. Boston: Kluwer Academic Publishers, c2002. International series in operations research & management science, 41. ISBN 0-7923-7495-9.


back to search page