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Lecturer(s)
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Prokop Roman, prof. Ing. CSc.
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Hrabec Dušan, Ing. Ph.D.
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Krňávek Jan, Mgr. Ph.D.
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Course content
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1. Multivariable function (properties). 2. Partial derivative, gradient. 3. Multivariable function (approximation, differential, Taylor polynomial). 4. Local extrema. 5. Constrained extrema. 6. Implicit function, derivative. 7. Linear programming. 8. Simplex method. 9. Primal and dual problem. 10. Integer programming (methods). 11. Integer programming problems. 12. Dynamic programming. 13. Dynamic programming problems. 14. 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
- 56 hours per semester
- Term paper
- 4 hours per semester
- Preparation for course credit
- 10 hours per semester
- Preparation for examination
- 20 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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| Lecturing |
| Lecturing |
| Practice exercises |
| Practice exercises |
| assessment methods |
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| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Analysis of seminar paper |
| Written examination |
| Written examination |
| Analysis of seminar paper |
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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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