Course detail

Optimization II

FSI-SO2-AAcad. year: 2024/2025

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

Mode of study

Not applicable.

Guarantor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 3rd  edition, Springer, 2011. (EN)
Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003. (EN)
Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010. (EN)
Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021. (EN)

Recommended reading

Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 2nd edition, Springer, 2011. (EN)
Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003. (EN)
King, A.J., Wallace, S.W.: Modeling with Stochastic Programming, Springer Verlag, 2014. (EN)
Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010. (EN)
Ruszczyński, A. and Shapiro, A. (Editors): Stochastic Programming, Handbook in Operations Research and Management Science. Elsevier Science, Amsterdam, 2003. (EN)
Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021. (EN)

Classification of course in study plans

  • Programme N-AIM-A Master's 2 year of study, winter semester, compulsory-optional
  • Programme N-MAI-A Master's 1 year of study, winter semester, compulsory

  • Programme C-AKR-P Lifelong learning

    specialization CZS , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., 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 hod., 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. 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.