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Course detail

Optimization - Mathematical Programming

Course unit code: FSI-9OMP
Academic year: 2016/2017
Year of study: Not applicable.
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
Students will learn fundamental theoretical knowledge about optimization modelling. The knowledge will be applied in applications.
Mode of delivery:
Not applicable.
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.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
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:
Czech, English
Work placements:
Not applicable.
Course curriculum:
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.

Type of course unit:

Lecture: 20 hours, 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)

The study programmes with the given course