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Lecturer(s)
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Pekař Libor, doc. Ing. Ph.D.
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Prokop Roman, prof. Ing. CSc.
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Krayem Said, prof. Ing. CSc.
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Course content
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1. Static optimization, objectives, history, basic concepts and notions, famous personalities and achievements. 2. Unconstrained problem, single and multivariable case. Derivatives, gradient, Hessian and Jacobian. 3. Constrained problem with a set of equalities. Lagrange method. 4. Nonlinear inequality constrained problem. Kuhn Tucker theorem. 5. Iterative methods withou derivatives, searching procedures. Fibbonaci method, Box - Wilson and Nelder - Mead methods. 6. Gradient methods, Gauss - Seidel method, Newton´s method. 7. Least - squares optimization. Gauss - Newton´s method, Levenberg - Marquart method. 8. Linear programming. Formulation and classification. 9. Basic simplex algorithm. Examples. 10. Advanced linear programming, mixed constraints. 11. Integer linear programming. Formulation and solution. 12. Dynamic programming. Bellman principle. . 13. Game theory. Basic concepts, classification. Reduction to linear programming. 14. Multiobjective, convex and decision problems.
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Learning activities and teaching methods
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Methods for written tasks (e.g. comprehensive exams, written tests), Demonstration, 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 Mahematics I and Maathematics II from bachelor study. Knowledge of calculas is necessary. |
| The course goes on to the course of Mahematics I and Maathematics II from bachelor study. Knowledge of calculas is necessary. |
| learning outcomes |
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| explain unconstrained and constrained optimization problems |
| explain unconstrained and constrained optimization problems |
| explain economic models for optimization purposes |
| explain economic models for optimization purposes |
| define the principle of simplex methods |
| define the principle of simplex methods |
| describe basic iterative methods of optimization |
| describe basic iterative methods of optimization |
| describe principles of game theory of two players |
| describe principles of game theory of two players |
| 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 |
| solve problems of matrix game theory of two players |
| solve problems of matrix game theory of two players |
| teaching methods |
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| Knowledge |
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| Exercises on PC |
| Exercises on PC |
| Demonstration |
| Methods for written tasks (e.g. comprehensive exams, written tests) |
| Methods for written tasks (e.g. comprehensive exams, written tests) |
| Demonstration |
| Individual work of students |
| Individual work of students |
| assessment methods |
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| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
| Analysis of seminar paper |
| Analysis of seminar paper |
| Analysis of a presentation given by the student |
| Analysis of a presentation given by the student |
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Recommended literature
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