Gurantor department | Department of Systems Engineering | Credits | 10 |

Subject guarantor | doc. Mgr. Ing. František Zapletal, Ph.D. | Subject version guarantor | doc. Mgr. Ing. František Zapletal, Ph.D. |

Study level | postgraduate | Requirement | Compulsory |

Year | Semester | winter + summer | |

Study language | English | ||

Year of introduction | 2020/2021 | Year of cancellation | |

Intended for the faculties | EKF | Intended for study types | Doctoral |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

ZAP149 | doc. Mgr. Ing. František Zapletal, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Examination | 28+0 |

Part-time | Examination | 28+0 |

The aim of this subject is to extend knowledge on and experience with mathematical modelling, with a special focus on optimization. Students will be able to solve complex optimization problems of convex, stochastic and fuzzy programming.

Lectures

Individual consultations

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.

SHAPIRO, Alexander, RUSZCZYNSKI Andrzej a kolektiv. Stochastic programming. Amsterdam: Elsevier, 2003. Handbooks in operations research and management science, v. 10. ISBN 0-444-50854-6.
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.

BIRGE, John R. a LOUVEAUX, François. Introduction to stochastic programming. 2nd ed. New York: Springer, c2011. Springer series in operations research. ISBN 978-1-4614-0236-7.
KALL, Peter a MAYER, János. 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 NISHIZAKI, Ichiro. Linear and multiobjective programming with fuzzy stochastic extensions. New York: Springer, c2013. International series in operations research & management science, 2013. ISBN 978-1-4614-9398-3.

The final evaluation of a student is based on his/her activity during the semester and results of the oral exam.

Information are provided to students at the lectures, through the LMS system. In LMS, there is an extended descriptions of the lectures and recommended literature.

Students must have a proactive approach and pass the oral exam.

Subject has no prerequisities.

Subject has no co-requisities.

1. Systemic approach, mathematical modelling,
2. Convex programming,
3. Logical constraints,
4. Risk measures,
5. Single-stage and multi-stage stochastic programming,
6. Multi-stage stochastic programming,
7. Chance-constrained programming,
8. Benders decomposition method,
9. Basics of fuzzy logic, algebra and set theory,
10. Possibilistic programming,
11. Flexible programming,
12. Intuitionistic fuzzy sets and their use in optimization.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
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Examination | Examination |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
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2020/2021 | (P0311D050020) Systems Engineering and Informatics | K | English | Ostrava | Compulsory | study plan | ||||||

2020/2021 | (P0311D050020) Systems Engineering and Informatics | P | English | Ostrava | Compulsory | study plan |

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