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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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- Economic models, system approach, cybernetic notions and tools. - Model and problem classification in operational analysis and research. - Analytical methods, unconstrained and constrained extrema, Lagrange function, Kuhn-Tucker theorem. - Lineár programming, simplex method, elimination principle and solutions. - Primal and dual problems. Duality aspects and interior point methods. - Integer linear programming. Bound and branch method. Gomory principle of cutting planes. - Dynamic programming, Bellman principle, rules for problems solution . - Decision theory, heuristics in decision, decision criteria ( minimax, Hurwitz, Laplace,...principles). - Conflict situations, game theory, games in explicit and normal forms. - Illustrative examples: Game of NIM, Take-away game, combinatorial games,... - Matrix games. Two person zero-sum games, proper and mixed strategies. - Graph solutions for game problems, solutions through linear programming. - Double matrix games. Dominance and dominated strategies. - Exaples of applied softwares (Wolfram Mathematica, Matlab).
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Learning activities and teaching methods
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Lecturing, Methods for working with texts (Textbook, book), Exercises on PC, Individual work of students
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| prerequisite |
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| Knowledge |
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| The course goes on to the course of Mahematic disciplins from batchelor study. Knowledge of basic notions (continuous function, derivative, matrix, algebraic equations,...) are necessary. |
| The course goes on to the course of Mahematic disciplins from batchelor study. Knowledge of basic notions (continuous function, derivative, matrix, algebraic equations,...) are necessary. |
| learning outcomes |
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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 method |
| define principle of simplex method |
| 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 |
| define basic statistical notions |
| define basic statistical notions |
| 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 extremes of real functions |
| find unconstrained and constrained extremes of real functions |
| define and solve the simplex algorithm |
| define and solve the simplex algorithm |
| 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 |
| apply basic statistical analysis tasks for data processing |
| apply basic statistical analysis tasks for data processing |
| teaching methods |
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| Knowledge |
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| Methods for working with texts (Textbook, book) |
| Lecturing |
| Lecturing |
| Individual work of students |
| Individual work of students |
| Exercises on PC |
| Methods for working with texts (Textbook, book) |
| Exercises on PC |
| assessment methods |
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| Analysis of seminar paper |
| Analysis of seminar paper |
| Written examination |
| Didactic test |
| Written examination |
| Didactic test |
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Recommended literature
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BARTKO, R. Matlab II.-Optimalizácia. VŠCHT Praha, 2008.
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FLETCHER, R. Practical Methods of Optimization. John Wiley 1987.
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GASS, S.I. Linear programming. Prentice Hall, 1982.
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HILLIER, F.S., LIEBERMAN, G.J. Introduction to Operational Research. McGraw-Hill, 2001.
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HUDZOVIČ, P. Optimalizácia. STU Bratislava, 2004.
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Maňas, M. Teorie her a optimálního rozhodování. Praha : SNTL, 1974.
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Prokop, R. Teória systémov a optimalizácia. Bratislava : SVŠT, 1990.
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