Optimization II (FSI-SO2-A)

Academic year 2021/2022
Supervisor: RNDr. Pavel Popela, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
The course objective is to develop the advanced knowledge of sophisticated optimization techniques as well as the understanding and applicability of principal concepts.
Learning outcomes and competences:
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.
Course contents:
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.
Teaching methods and criteria:
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.
Controlled participation in lessons:
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  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture 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 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.
Literature - fundamental:
1. Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003.
2. Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 3rd  edition, Springer, 2011.
3. Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010.
Literature - recommended:
1. King, A.J., Wallace, S.W.: Modeling with Stochastic Programming, Springer Verlag, 2014.
2. Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003.
3. Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 2nd edition, Springer, 2011.
4. Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021.
5. Ruszczyński, A. and Shapiro, A. (Editors): Stochastic Programming, Handbook in Operations Research and Management Science. Elsevier Science, Amsterdam, 2003.
6. Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-AIM-A full-time study --- no specialisation -- Cr,Ex 4 Compulsory-optional 2 2 W
N-MAI-A full-time study --- no specialisation -- Cr,Ex 4 Compulsory 2 2 W
M2A-A full-time study M-MAI Mathematical Engineering -- Cr,Ex 4 Compulsory 2 2 W
N-MAI-A full-time study --- no specialisation -- Cr,Ex 4 Compulsory 2 1 W