Course detail
Optimization II
FSI-SO2 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 network flows, integer and dynamic programming.
Language of instruction
Czech
Number of ECTS credits
4
Supervisor
Department
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
The exam is based on presentation of prepared paper and following joint 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 advanced 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-MAI-P: 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. 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 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.