Course detail

Optimization - Mathematical Programming

FSI-9OMPAcad. year: 2024/2025

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

Mode of study

Not applicable.

Guarantor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

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

Rules for evaluation and completion of the course

The exam runs in the form of workshop. The paper oral and written presentation is required and specialized discussion is assumed.


The faculty rules are applied.

Aims

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

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

Study aids

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
Bazaraa M. et al.: Linear Programming and Network Flows,. John Wiley and Sons, 2011
Bazaraa, M. et al.: Nonlinear Programming,, John Wiley and Sons, 2012
]Boyd, S. and Vandeberghe, L.: Convex Optimization. Cambridge: Cambridge University Press, 2004
Popela,P.: Lineární programování v kostce. sylabus, 2015, PDF
Popela,P.: Nonlinear programming. VUT sylabus, 2021, PDF

Classification of course in study plans

  • Programme D-ENE-P Doctoral 1 year of study, winter semester, recommended course
  • Programme D-ENE-K Doctoral 1 year of study, winter semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

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)