Optimization - Mathematical Programming (FSI-9OMP)

Academic year 2022/2023
Supervisor: RNDr. Pavel Popela, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The course is focused on knowledge useful for engineering optimization models. Motivation of presented concepts is emphasized.
Learning outcomes and competences:
Students will learn fundamental theoretical knowledge about optimization modelling. The knowledge will be applied in applications.
Prerequisites:
Introductory knowledge of mathematical modelling of engineering systems.
Basic MSc. knowledge of Calculus, linear algebra, probability, statistics and numerical methods applied to engineering disciplines.
Course contents:
The solution of many actual engineering problems cannot be achieved without the knowledge of mathematical foundations of optimization.
The course focuses on mathematical programming areas. The presented material is related to theory (convexity, linearity, differentiability, and stochasticity), algorithms (deterministic, stochastic, heuristic), the use of
specialized software, and modelling. All important types of mathematical models are discussed, involving linear, discrete, convex, multicriteria and stochastic. Every year, the course is updated by including the recent topics related to areas interests of students.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
The exam runs in the form of workshop. The paper oral and written presentation is required and specialized discussion is assumed.
Controlled participation in lessons:
The faculty rules are applied.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 1. Basic models
2. Linear models
3. Special (network flow and integer) models
4. Nonlinear models
5. General models (parametric, multicriteria, nondeterministic,
dynamic, hierarchical)
Literature - fundamental:
1. Bazaraa,M. et al.: Nonlinear Programming. Wiley and Sons
2. Paradalos et al.: Handbook of Optimization. Wiley and Sons
3. Williams,H.P.: Model Building in Mathematical Programming. Wiley and Sons
Literature - recommended:
1. Klapka,J. a kol.: Metody operačního výzkumu. FSI 2001
2. Popela,P.: Nonlinear programming. VUT sylabus, 2021, PDF
3. Popela,P.: Lineární programování v kostce. sylabus, 2015, PDF
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-ENE-P full-time study --- no specialisation -- DrEx 0 Recommended course 3 1 W
D-ENE-K combined study --- no specialisation -- DrEx 0 Recommended course 3 1 W