Course detail

Optimization - Mathematical Programming

FSI-9OMPAcad. year: 2016/2017

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.

Language of instruction

Czech

Number of ECTS credits

1

Learning outcomes of the course unit

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.

Co-requisites

Not applicable.

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.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Bazaraa,M. et al.: Nonlinear Programming. Wiley and Sons
Paradalos et al.: Handbook of Optimization. Wiley and Sons
Williams,H.P.: Model Building in Mathematical Programming. Wiley and Sons

Recommended reading

Klapka,J. a kol.: Metody operačního výzkumu. FSI 2001
Popela,P.: Nonlinear programming. VUT sylabus, 2021, PDF
Popela,P.: Lineární programování v kostce. sylabus, 2015, PDF

Type of course unit

 

Lecture

20 hours, optionally

Teacher / Lecturer

Syllabus

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