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

Subject guarantor | prof. RNDr. Zdeněk Dostál, DSc. | Subject version guarantor | prof. RNDr. Zdeněk Dostál, DSc. |

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2003/2004 | Year of cancellation | 2009/2010 |

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. |

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 | 2+3 |

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.

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 on unconstrained optimization (45 minutes, max 10 marks).
Written exam on constrained optimization (45 minutes, max 10 marks).
Conditions for credit:
At least 25 marks on progress assessment and projects.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
An introduction to the calculus of variations. Linear spaces, funkcionls and their differentials (Fréchet, Gateaux).
Euler equation and the solution of the classical problems of variational calculus.
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods, method of conjugate gradients.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization and barrier methods for constrained minimization. Feasible direction method (SLP) and active set strategy for bound constrained problems.
Duality in convex programming. Saddle points, Uzawa algorithm and augmented Lagrangians.
Linear programming, simplex method.
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 conjugate gradient method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the feasible direction method (SLP).
Implementation of the active set method for bound constrained quadratic programming.
Implementation of the augmented Lagrangian metod.
Implementation of algorithms for global optimization.
Solution of selected engeneering problems using optimization software.
Projects:
Comparing performance of the methods for unconstrained optimization using a numerical example (max 10 marks).
Comparing performance of the methods for constrained optimization using a numerical example (max 10 marks).
Solution of a selected engineering problem (max 10 marks).
Computer labs:
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 conjugate gradient method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the feasible direction method (SLP).
Implementation of the active set method for bound constrained quadratic programming.
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 | 3 |

Examination | Examination | 70 | 0 | 3 |

Exercises evaluation | Credit | 30 | 0 |

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

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Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2009/2010 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2009/2010 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2008/2009 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2008/2009 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2007/2008 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2007/2008 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2006/2007 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2006/2007 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2005/2006 | (N2646) Information Technology | (1103T021) Computational Mathematics | P | Czech | Ostrava | 3 | Compulsory | study plan | ||||

2005/2006 | (N2646) Information Technology | (1103T021) Computational Mathematics | K | Czech | Ostrava | 3 | Compulsory | study plan | ||||

2004/2005 | (N2646) Information Technology | (1103T021) Computational Mathematics | P | Czech | Ostrava | 3 | Compulsory | study plan | ||||

2004/2005 | (N2646) Information Technology | (1103T021) Computational Mathematics | K | Czech | Ostrava | 3 | Compulsory | study plan |

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