Course detail

Optimization II

FSI-SO2-A Acad. year: 2023/2024 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

English

Number of ECTS credits

4

Entry knowledge

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

Rules for evaluation and completion of the course

There is an exam based on presentation of a written theme accompanied by oral discussion of results.


The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.

Aims

The course objective is to develop the advanced knowledge of sophisticated optimization techniques as well as the understanding and applicability of principal concepts.


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.

The study programmes with the given course

Programme N-AIM-A: Applied and Interdisciplinary Mathematics, Master's, compulsory-optional

Programme N-MAI-A: Mathematical Engineering, Master's, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

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

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. Network flows.
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.