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Lecturer(s)
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Prokop Roman, prof. Ing. CSc.
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Pekař Libor, doc. Ing. Ph.D.
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Course content
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- Economic models, system concepts, cybernetics and resources. - Types of models and classification of tasks in the field of operational analysis. - Linear programming, simplex table, elimination procedure and problem solving. - Primary and dual role. Aspects of duality and ambiguity. - Integer programming, methods of cutting surfaces (Gomory). - Dynamic programming, Bellman's principle, solution methods. - Decision theory, decision making under uncertainty, decision criteria (minimax principle, Hurwitz, Laplace,?). - Conflict situations, classification of game theory problems, games in explicit form. - Games in normal form. Antagonistic conflict between two players, single-matrix games, pure and mixed strategies. - Graphic solution of selected tasks, solution using linear programming. - Two-matrix games. Dominant and dominant strategies. - Cooperative and non-cooperative games, duopoly and oligopoly, differential games. - Examples of application software (Mathematica, Matlab).
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Learning activities and teaching methods
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unspecified
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| learning outcomes |
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| Knowledge |
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| define unconstrained and constrained optimization problems |
| define unconstrained and constrained optimization problems |
| explain relations between derivations and extrema of real functions |
| explain relations between derivations and extrema of real functions |
| define principle of simplex methods |
| define principle of simplex methods |
| explain economic models for optimization purposes |
| explain economic models for optimization purposes |
| describe principles of game theory of two players |
| describe principles of game theory of two players |
| describe basic iterative methods of optimization |
| describe basic iterative methods of optimization |
| Skills |
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| solve derivatives and partial derivatives of real functions |
| solve derivatives and partial derivatives of real functions |
| find unconstrained and constrained extrema of real functions |
| find unconstrained and constrained extrema of real functions |
| define and solve the simplex tableau |
| define and solve the simplex tableau |
| solve economic problems by linear and dynamic programming |
| solve economic problems by linear and dynamic programming |
| formulate and solve problems of matrix game theory of two players |
| formulate and solve problems of matrix game theory of two players |
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Recommended literature
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ANTONIOU, A. and W.S. LU. Practical Optimization. Springer-Verlag, 2007. ISBN 0-387-71106-6.
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FLETCHER, R. Practical Methods of Optimization. Wiley, 2000. ISBN 978-0-471-49463-6.
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GILL, P.E., MURAY, W. and M.H. WRIGHT. Practical Optimization. Academic Press, London, 1981.
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JABLONSKÝ, J. Operační výzkum. Professional Publishing, Praha, 2002.
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PEKAŘ, L. Optimalizace, studijní materiály. FAI UTB, Zlín, 2013.
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PROKOP, R. Optimalizace. FAI, UTB, 2015.
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