Course detail

Optimization II

FSI-SO2 Acad. year: 2020/2021 Winter semester

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.

Language of instruction

Czech

Number of ECTS credits

4

Supervisor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics

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.

Prerequisites

The presented topics require basic knowledge of optimization concepts (see SOP).
Standard knowledge of probabilistic and statistical concepts is assumed.

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.

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.

The study programmes with the given course

Programme M2A-P: Applied Sciences in Engineering, Master's
branch M-MAI: Mathematical Engineering, compulsory

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.

Computer-assisted exercise

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.

Course participance is obligatory.