Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | doc. Ing. Petr Beremlijski, Ph.D. | Subject version guarantor | doc. Ing. Petr Beremlijski, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

BER95 | doc. Ing. Petr Beremlijski, Ph.D. | ||

DOS35 | prof. RNDr. Zdeněk Dostál, DSc. | ||

SAD015 | Ing. Marie Sadowská, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

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.

Lectures

Tutorials

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.

D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont 1999. ISBN 1-886529-00-0.
M. S: Bazaraa, C. M. Shetty, Nonlinear programming, J. Wiley, New York 1979, ruský překlad Mir Moskva 1982.
R. Fletcher, Practical Methods of Optimization, John Wiley & sons,Chichester 1997.

D. T. Pham and D. Karaboga, Intelligent Optimization Techniques, Springer, London 2000. ISBN 1-85233-028-7.
Z. Dostal, Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities Springer, New York 2009. ISBN: 0387848053, ISBN-13: 9780387848051

Verification of study:
Written exam (max 10 marks).
Project (max 20 marks)
Conditions for credit:
Minimum 10 marks on tests and project.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

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.
Duality in convex programming. Saddle points, Uzawa algorithm and augmented Lagrangians.
Non-smooth optimization, subgradients and optimality conditions.
Global optimization, genetic and evolutionary algorithms, simulated annealing, tabu search.
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.
Implementation of algorithms for global optimization.
Solution of selected engeneering problems using optimization software.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 | |

Exercises evaluation | Credit | 30 | 15 | |

Examination | Examination | 70 | 21 | 3 |

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Conditions for subject completion and attendance at the exercises within ISP:

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Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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