Optimisation

Summary

The subject is divided into 4 parts, in which various subfields of optimization are explored:
A) Non-linear models and existence of their optimal solution (convex programming), Bender's decomposition.
B) Logical relationships between decision variables and constraints (OR, XOR, implication).
C) Stochastic programming - optimization with random parameters (static models, dynamic models - multi-stage models, non-anticipativity constraints, static and dynamic risk measures, coherent, convex and time-consistent risk measures,
D) fuzzy programming - optimization under uncertainty (with fuzzy parameters and relations - a way how to involve qualitative and subjective data.

Literature

SHAPIRO, Alexander a Andrzej RUSZCZYNSKI, ed. Stochastic programming. Amsterdam: Elsevier, 2003. Handbooks in operations research and management science, v. 10. .
FIEDLER, Miroslav. Linear optimization problems with inexact data. New York: Springer, c2006. 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

BIRGE, John R. a François LOUVEAUX. Introduction to stochastic programming. 2nd ed. New York: Springer, c2011. Springer series in operations research. ISBN 978-1-4614-0236-7.
KALL, Peter a János MAYER. Stochastic linear programming: models, theory, and computation. 2nd ed. New York: Springer, c2011. International series in operations research & management science, 156. ISBN 978-1-4419-7728-1.
SAKAWA, Masatoshi, Hitoshi YANO a Ichiro NISHIZAKI. Linear and multiobjective programming with fuzzy stochastic extensions. New York: Springer, c2013. International series in operations research & management science, 203. ISBN 978-1-4614-9398-3.

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Language of instruction	čeština
Code	157-9986
Abbreviation	O
Course title	Optimisation
Coordinating department	Department of Systems Engineering and Informatics
Course coordinator	prof. Mgr. Ing. František Zapletal, Ph.D.