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
Mode of study
Guarantor
Department
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
Students will learn fundamental theoretical knowledge about optimization modelling. The knowledge will be applied in applications.
Study aids
Prerequisites and corequisites
Basic literature
Paradalos et al.: Handbook of Optimization. Wiley and Sons
Williams,H.P.: Model Building in Mathematical Programming. Wiley and Sons
Recommended reading
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
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Linear models
3. Special (network flow and integer) models
4. Nonlinear models
5. General models (parametric, multicriteria, nondeterministic,
dynamic, hierarchical)