157-9986/01 – Optimisation (O)

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	Czech
Year of introduction	2020/2021	Year of cancellation
Intended for the faculties	EKF	Intended for study types	Doctoral

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
ZAP149	doc. Mgr. Ing. František Zapletal, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Examination	28+0
Part-time	Examination	28+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Individual consultations

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.

Compulsory literature:

SHAPIRO, Alexander a Andrzej RUSZCZYNSKI, ed. 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.

Recommended 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.

Way of continuous check of knowledge in the course of semester

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

E-learning

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.

Other requirements

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

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Full-time form (validity from: 2020/2021 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Examination	Examination			3

Mandatory attendence participation:

Show history

Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic year	Programme	Form	Study language	Tut. centre	Type of duty
2024/2025	(P0311D050019) Systems Engineering and Informatics	P	Czech	Ostrava	Compulsory	study plan
2024/2025	(P0311D050019) Systems Engineering and Informatics	K	Czech	Ostrava	Compulsory	study plan
2023/2024	(P0311D050019) Systems Engineering and Informatics	P	Czech	Ostrava	Compulsory	study plan
2023/2024	(P0311D050019) Systems Engineering and Informatics	K	Czech	Ostrava	Compulsory	study plan
2022/2023	(P0311D050019) Systems Engineering and Informatics	K	Czech	Ostrava	Compulsory	study plan
2022/2023	(P0311D050019) Systems Engineering and Informatics	P	Czech	Ostrava	Compulsory	study plan
2021/2022	(P0311D050019) Systems Engineering and Informatics	P	Czech	Ostrava	Compulsory	study plan
2021/2022	(P0311D050019) Systems Engineering and Informatics	K	Czech	Ostrava	Compulsory	study plan
2020/2021	(P0311D050019) Systems Engineering and Informatics	P	Czech	Ostrava	Compulsory	study plan
2020/2021	(P0311D050019) Systems Engineering and Informatics	K	Czech	Ostrava	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

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