Course detail
Optimization
FIT-OPMAcad. year: 2023/2024
The course presents fundamental optimization models and methods for solving of technical problems. The principal ideas of mathematical programming are discussed: problem analysis, model building, solution search, and the interpretation of results. The course mainly deals with linear programming (polyhedral sets, simplex method, duality) and nonlinear programming (convex analysis, Karush-Kuhn-Tucker conditions, selected algorithms). Basic information about network flows and integer programming is included as well as further generalizations of studied mathematical programs.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Entry knowledge
Rules for evaluation and completion of the course
The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.
Aims
The course is designed for mathematical engineers and it is useful for applied sciences students. Students will learn the theoretical background of fundamental topics in optimization (especially linear and non-linear programming). They will also made familiar with useful algorithms and interesting applications.
Study aids
Prerequisites and corequisites
Basic literature
Recommended reading
Bazaraa et al.: Nonlinear Programming, Wiley 1993.
Charamza a kol.: Modelovací systém GAMS, Praha 1994.
Klapka a kol.: Metody operačního výzkumu, Brno 2001.
Classification of course in study plans
- Programme IT-MSC-2 Master's
branch MMM , 0 year of study, summer semester, compulsory-optional
branch MBS , 0 year of study, summer semester, elective
branch MPV , 0 year of study, summer semester, elective
branch MBI , 0 year of study, summer semester, elective
branch MSK , 0 year of study, summer semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Introductory models (IM): problem formulation, problem analysis, model design, theoretical properties.
- IM: visualization, algorithms, software, postprocessing in optimization
- Linear programming (LP): Convex and polyhedral sets.
- LP: Set of feasible solutions and theoretical foundations.
- LP: The Simplex method.
- LP: Duality and parametric analysis.
- Network flow models.
- Basic concepts of integer programming.
- Nonlinear programming (NLP): Convex functions and their properties.
- NLP: Unconstrained optimization. Numerical methods for univariate optimization.
- NLP: Unconstrained optimization and related numerical methods for multivariate optimization.
- NLP: Constrained optimization and Karush-Kuhn-Tucker conditions.
- NLP: Constrained optimization and related numerical methods for multivariate optimization.
Exercise in computer lab
Teacher / Lecturer
Syllabus
- Cvičení 1-2: Úvodní úlohy
- Cvičení 2-7: Lineární úlohy
- Cvičení 7-8: Speciální úlohy
- Cvičení 9-13: Nelineární úlohy