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Course detail

Optimization II

Course unit code: FSI-SO2
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Master's (2nd cycle)
Year of study: 1
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
The course is mainly designated for mathematical engineers, however it might be useful for applied sciences students as well. Students will learn of the recent theoretical topics in optimization and advanced optimization algorithms. They will also develop their ideas about suitable models for typical applications.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
The presented topics require basic knowledge of optimization concepts (see SOP). Standard knowledge of probabilistic and statistical concepts is assumed.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
The course focuses on advanced optimization models and methods of solving engineering problems. It includes especially stochastic programming (deterministic reformulations, theoretical properties, and selected algorithms) and selected areas of integer and dynamic programming.
Recommended or required reading:
Kall, P.-Wallace,S.W.: Stochastic Programming, Wiley 1994.
Klapka, J. a kol: Metody operačního výzkumu, VUT, 2000.
Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, Springer, 1997.
Prekopa, A: Stochastic Programming, Kluwer, 1996.
Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
There is a written exam accompanied by oral discussion of results.
Language of instruction:
Czech
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
The course objective is to develop the advanced knowledge of sophisticated optimization techniques as well as the understanding and applicability of principal concepts.
Specification of controlled education, way of implementation and compensation for absences:
The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.

Type of course unit:

Lecture: 26 hours, optionally
Teacher / Lecturer: RNDr. Pavel Popela, Ph.D.
Syllabus: 1. Underlying mathematical program.
2. WS and HN approach.
3. IS and EV reformulations.
4. EO, EEV, EVPI and VSS.
5. MM and VO, the solution of the large problems.
6. PO and QO, relation to integer programming.
7. Deterministic and probabilistic constraints, the use of recourse.
8. WS theory - convexity and measurability.
9. WS theory - probability distribution identification.
10. Twostage problems, classification and modelling.
11. Basic results in convexity of SPs.
12. Applied twostage programming.
13. Dynamic programming and multistage models.
seminars in computer labs: 13 hours, compulsory
Teacher / Lecturer: RNDr. Pavel Popela, Ph.D.
Syllabus: Exercises on:
1. Underlying mathematical program.
2. WS and HN approach.
3. IS and EV reformulations.
4. EO, EEV, EVPI and VSS.
5. MM and VO, the solution of the large problems.
6. PO and QO, relation to integer programming.
7. Deterministic and probabilistic constraints, the use of recourse.
8. WS theory - convexity and measurability.
9. WS theory - probability distribution identification.
10. Twostage problems, classification and modelling.
11. Basic results in convexity of SPs.
12. Applied two-stage programming.
13. Dynamic programming and multistage models.

The study programmes with the given course