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Lecturer(s)
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Krayem Said, prof. Ing. CSc.
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Hrabec Dušan, Ing. Ph.D.
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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
- Term paper
- 10 hours per semester
- Preparation for examination
- 20 hours per semester
- Participation in classes
- 56 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| 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) |
| Written examination |
| Written examination |
| Grade (Using a grade system) |
| Analysis of seminar paper |
| Analysis of seminar paper |
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Recommended literature
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Dantzig, George Bernard. Lineárne programovanie a jeho rozvoj. 1. vyd. Bratislava : Slovenské vydavateĺstvo technickej literatúry, 1966.
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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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Matoušek, J. a Gartner, B. Understanding and using Linear Programming. Springer Berlin Heidelberg, 2007. ISBN 78-3-540-30697-9.
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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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Ravindran, A., Ragsdell, K.M. a Reklaitis, G.V. Engineering Optimization: Methods and Applications, 2nd Edition. Wiley, 2006. ISBN 978-0-471-55814-9.
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Vanderbei, R.J. Linear programming: foundations and extensions. New York: Springer, 2013. ISBN 978-1-4614-7629.
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WEIR, Maurice D., Joel. HASS, George B. THOMAS, and Ross L. FINNEY. Thomas' calculus. Boston, 2008. ISBN 032148987X.
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