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Main menu for Browse IS/STAG
Course info
KMA / MNO
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Course description
Department/Unit / Abbreviation
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KMA
/
MNO
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Numerical Optimization Methods
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
4
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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7 / -
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2 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KMA/NMO
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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1. Basic optimization problems - from antiquity to modern engineering optimization problems. Statement of problems of linear and non-linear problems.
2. Classical optimization techniques and optimality conditions. Unconstrained numerical techniques (gradient methods, quasi-Newton methods).
3. Optimality conditions for contrained equality problems.Linear and quadratic optimization), Lagrange princip.
4. Constrained numerical techniques for non-equality problems. Duality .
5. Optimization problems in technologies
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Requirements on student
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It is necessary to prepare and present (and submit within the deadline) given tasks. The implementation of specific tasks is in the MATLAB environment.
The exam consists of a written and oral part based on the elaboration of given tasks, a discussion of these tasks, the ability to formulate problems and the corresponding conditions of optimality and interpretation of a particular method.
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Content
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1. Optimization - Introduction.
2. Basic properties of solution (necessary and sufficient conditions, convexity).
3. Line search.
4. Basic methods (Steepest Descent method, Newton method).
5. Conjugate direction methods.
6. Quasi-Newton methods.
7. Trust region methods.
8. Least square problem.
9. Nonvariational methods.
10. Constrained optimization.
11. Linear programming, simplex method.
12. Some methods for constrained optimization.
13. Revision for exam.
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Activities
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Fields of study
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Studentům je k dispozici kurz v Google Classroom se všemi materiály a informacemi.
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Guarantors and lecturers
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Literature
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Basic:
Matematická optimalizace
(Míka, Stanislav)
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Basic:
Lukšan, Ladislav. Metody s proměnnou metrikou : Nepodmíněná minimalizace. 1. vyd. Praha : Academia, 1990. ISBN 80-200-0211-1.
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Recommended:
Dostál Z., Beremlijski P. Metody optimalizace. VŠB-TU Ostrava a ZČU v Plzni, 2012.
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Recommended:
Machalová J., Netuka H. Nelineární programování: teorie a metody. Univerzita Palackého v Olomouci, 2013.
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Recommended:
Nocedal J., Wright S. Numerical Optimization, Second edition. Springer Verlag, 2006.
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Recommended:
Machalová J., Netuka H. Numerické metody nepodmín?né optimalizace. Univerzita Palackého v Olomouci, 2013.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Presentation preparation (report) (1-10)
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10
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Preparation for an examination (30-60)
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55
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Contact hours
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39
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Total
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104
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
formulovat základní optimalizační úlohy na maximum, resp. minimum |
charakterizovat základní vlastnosti posloupností, řad a spojitých a diferencovatelných funkcí jedné reálné proměnné |
vysvětlit a popsat principy diferenciálního a integrálního počtu funkcí jedné i více reálných proměnných |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
určit Taylorův rozvoj dané funkce v blízkosti daného bodu |
vypočítat derivaci funkce jedné proměnné a derivace ve směru a parciální derivace funkcí více proměnných |
vypočítat hodnotu určitého integrálu a kvadraturu aplikovat pro výpočet povrchu a objemu jednoduchých těles |
vyšetřit průběh funkce s použitím asymptot, kritických bodů a derivací pro určení intervalů monotonie a konvexity, resp. konkavity |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
definovat podmínky optimality v úlohách podmíněné optimalizace s vazbami typu rovnosti a nerovnosti |
formulovat elementární úlohy lineární a nelineární optimalizace s vazbami a bez vazeb, charakterizovat typy přípustných množin |
popsat metody hladké (klasické) optimalizace |
popsat princip dualizace optimalizačních úloh a definovat úlohu sedlového bodu |
Skills - skills resulting from the course: |
aplikovat spádové, gradientní a kvazinewtonovské metody na řešení konkrétních problémů |
používat softwarové systémy typu MATLAB |
využívat znalostí pro řešení optimalizačních úloh v technice a ekonomii (např. úlohy optimálního řízení, dopravní problém, problém obchodního cestujícího, úlohy teorie her) |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Textual studies |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Students' portfolio |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Task-based study method |
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