| Course Unit Code | 470-8742/01 |
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| Number of ECTS Credits Allocated | 3 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type B |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| DOS35 | prof. RNDr. Zdeněk Dostál, DSc. |
| BER95 | doc. Ing. Petr Beremlijski, Ph.D. |
| Summary |
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| Optimization methods are basic tools for improving design and technology. The students will learn about basic optimization problems, conditions of their solvability and correct formulation. Effective algorithms, heuristics and software will be presented in an extent that is useful for the soluving engineering problems. |
| Learning Outcomes of the Course Unit |
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| The student will be able to recognize basic classes of optimization problems and will understand conditions of their solvability and correct formulation. Effective algorithms, heuristics and software will be presented in an extent that is useful for solving engineering problems, so that the student will be able to apply their knowledge to the solution of practical problems. |
| Course Contents |
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Lectures:
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization methods for constrained minimization. Augmented Lagrangians
Duality in convex programming. Saddle points.
Non-smooth optimization, subgradients and optimality conditions.
Software.
Exercises:
Introduction to the MATLAB programming.
Implementation of the golden section and Fibonacci series methods.
Implemenation of the Newton-like methods.
Implementation of the gradient based method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the augmented Lagrangian metod.
Solution of selected engeneering problems using optimization software. |
| Recommended or Required Reading |
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| Required Reading: |
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BERTSEKAS, Dimitri P. Nonlinear Programming. 3rd edition. Athena Scientific, 2016. ISBN 978-1886529052.
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DOSTÁL, Zdeněk a Petr BEREMLIJSKI. Metody optimalizace [online]. VŠB-TU Ostrava, 2012 [cit. 2024-04-17]. Dostupné z: https://mi21.vsb.cz/modul/metody-optimalizace
DUPAČOVÁ, Jitka a LACHOUT, Petr. Úvod do optimalizace. Praha: Matfyzpress, 2011. ISBN 978-80-7378-176-7.
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| Recommended Reading: |
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NOCEDAL, Jorge a Stephen WRIGHT. Numerical Optimization. 2nd edition. Springer, 2006. ISBN 978-0387303031.
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KOŘENÁŘ, Václav a LAGOVÁ, Milada. Optimalizační metody. V Praze: Oeconomica, 2003. ISBN 8024506092.
ŽENČÁK, Pavel. Lineární programování. Olomouc: Univerzita Palackého v Olomouci, 2013. ISBN 978-80-244-3414-8.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 30 | 15 |
| Examination | Examination | 70 | 21 |