Course detail

Optimization - Mathematical Programming

FSI-9OMPAcad. year: 2016/2017Winter semesterNot applicable.. year of study1  credit

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.

Learning outcomes of the course unit

Students will learn fundamental theoretical knowledge about optimization modelling. The knowledge will be applied in applications.


Introductory knowledge of mathematical modelling of engineering systems. Basic MSc. knowledge of Calculus, linear algebra, probability, statistics and numerical methods applied to engineering disciplines.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Bazaraa,M. et al.: Nonlinear Programming. Wiley and Sons
Klapka,J. a kol.: Metody operačního výzkumu. FSI 2001
Popela,P._: Nonlinear programming. sylabus, PDF
Paradalos et al.: Handbook of Optimization. Wiley and Sons
Popela,P.: Lineární programování v kostce. sylabus, PDF
Williams,H.P.: Model Building in Mathematical Programming. Wiley and Sons

Planned learning activities and teaching methods

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.

Language of instruction


Work placements

Not applicable.


The course is focused on knowledge useful for engineering optimization models. Motivation of presented concepts is emphasized.

Specification of controlled education, way of implementation and compensation for absences

The faculty rules are applied.

Type of course unit



20 hours, optionally

Teacher / Lecturer


1. Basic models
2. Linear models
3. Special (network flow and integer) models
4. Nonlinear models
5. General models (parametric, multicriteria, nondeterministic,
dynamic, hierarchical)