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Lecturer(s)
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Prokop Roman, prof. Ing. CSc.
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Course content
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- Multivariable function (properties). - Partial derivative, gradient. - Multivariable function (approximation, differential, Taylor polynomial). - Local extrema. - Constrained extrema. - Implicit function, derivative. - Linear programming. - Simplex method. - Primal and dual problem. - Integer programming (methods). - Integer programming problems. - Dynamic programming. - Dynamic programming problems. - Applications and software (GAMS, AMPL, Wolfram Mathematica, Matlab).
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Learning activities and teaching methods
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Lecturing, Practice exercises
- Participation in classes
- 20 hours per semester
- Preparation for examination
- 40 hours per semester
- Term paper
- 30 hours per semester
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| prerequisite |
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| Knowledge |
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| The basic knowledge of linear algebra, mathematical analysis and differential calculus is considered. |
| The basic knowledge of linear algebra, mathematical analysis and differential calculus is considered. |
| learning outcomes |
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| Students will learn to use mathematical methods, modeling, and algorithmic approaches to solve problems that appear when searching for optimal solutions to practical problems (e.g., managerial, decision-making, and logistics). Particularly: |
| Students will learn to use mathematical methods, modeling, and algorithmic approaches to solve problems that appear when searching for optimal solutions to practical problems (e.g., managerial, decision-making, and logistics). Particularly: |
| - to describe the basic properties of multivariable functions and principles of differential calculus of the functions, |
| - to describe the basic properties of multivariable functions and principles of differential calculus of the functions, |
| - to characterize and analyze assigned tasks and suggest known solution approaches, |
| - to characterize and analyze assigned tasks and suggest known solution approaches, |
| - to know the principles and categories of mathematical optimization (e.g., linear and integer programming and their properties) and know to assign the problem to a particular class of mathematical optimization, |
| - to know the principles and categories of mathematical optimization (e.g., linear and integer programming and their properties) and know to assign the problem to a particular class of mathematical optimization, |
| - to know solution approaches and, based on properties of the mathematical model, suggest a solution approach and alternatively solve the problem, |
| - to know solution approaches and, based on properties of the mathematical model, suggest a solution approach and alternatively solve the problem, |
| - knowledge of some selected existing solvers and software used to solve optimization problems. |
| - knowledge of some selected existing solvers and software used to solve optimization problems. |
| Skills |
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| Analyze multivariable functions and differential calculus of the functions |
| Analyze multivariable functions and differential calculus of the functions |
| Characterize and analyze assigned tasks and suggest a solution approach |
| Characterize and analyze assigned tasks and suggest a solution approach |
| Create a mathematical model of the assigned problem from mathematical optimization (especially in linear and integer programming) and assign the problem to a particular class of mathematical optimization |
| Create a mathematical model of the assigned problem from mathematical optimization (especially in linear and integer programming) and assign the problem to a particular class of mathematical optimization |
| Know, based on properties of the mathematical model, to suggest a solution approach and to solve the problem |
| Know, based on properties of the mathematical model, to suggest a solution approach and to solve the problem |
| To know some selected existing solvers and software used to solve optimization problems |
| To know some selected existing solvers and software used to solve optimization problems |
| teaching methods |
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| Knowledge |
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| Practice exercises |
| Lecturing |
| Lecturing |
| Practice exercises |
| assessment methods |
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| Written examination |
| Grade (Using a grade system) |
| Written examination |
| Analysis of seminar paper |
| Analysis of seminar paper |
| Grade (Using a grade system) |
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Recommended literature
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DUPAČOVÁ, J. a LACHOUT, P. Úvod do optimalizace. MFF UK v Praze, 2011. ISBN 978-80-7378-176-7.
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HRABEC, D. Optimalizace, studijní materiály, přednáškové slidy. Zlín, 2018.
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Klapka, J., Dvořák, J. a Popela, P. Metody operačního výzkumu. VUT v Brně, 2001. ISBN 80-214-1839-7.
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KUBIŠOVÁ, A. Operační výzkum. Vysoká škola polytechnická Jihlava, 2014. ISBN 978-80-87035-83-2.
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NOVOTNÝ, J. Základy operačního výzkumu. FAST VUT v Brně, 2006.
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Ostravský, J. Diferenciální počet funkce více proměnných. Nekonečné číselné řady. Zlín : UTB, 2007. ISBN 978-80-7318-567-1.
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PEKAŘ, L. Optimalizace, studijní materiály, přednášky. Zlín, 2013.
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