Course: Numerical Optimization Methods

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Course title Numerical Optimization Methods
Course code KMA/MNO
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Daněk Josef, Doc. Ing. Ph.D.
  • Kopincová Hana, Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
  • Turnerová Eva, Ing.
Course content
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.

Learning activities and teaching methods
Interactive lecture, Lecture with practical applications, Students' portfolio, Task-based study method, Textual studies
  • Presentation preparation (report) (1-10) - 10 hours per semester
  • Contact hours - 39 hours per semester
  • Preparation for an examination (30-60) - 55 hours per semester
prerequisite
professional knowledge
vysvětlit a popsat principy diferenciálního a integrálního počtu funkcí jedné i více reálných proměnných
formulovat základní optimalizační úlohy na maximum, resp. minimum
charakterizovat základní vlastnosti posloupností, řad a spojitých a diferencovatelných funkcí jedné reálné proměnné
professional skills
určit Taylorův rozvoj dané funkce v blízkosti daného bodu
vyšetřit průběh funkce s použitím asymptot, kritických bodů a derivací pro určení intervalů monotonie a konvexity, resp. konkavity
vypočítat hodnotu určitého integrálu a kvadraturu aplikovat pro výpočet povrchu a objemu jednoduchých těles
vypočítat derivaci funkce jedné proměnné a derivace ve směru a parciální derivace funkcí více proměnných
general eligibility
N/A
N/A
learning outcomes
professional knowledge
formulovat elementární úlohy lineární a nelineární optimalizace s vazbami a bez vazeb, charakterizovat typy přípustných množin
popsat metody hladké (klasické) optimalizace
definovat podmínky optimality v úlohách podmíněné optimalizace s vazbami typu rovnosti a nerovnosti
popsat princip dualizace optimalizačních úloh a definovat úlohu sedlového bodu
professional skills
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)
general eligibility
N/A
teaching methods
professional knowledge
Interactive lecture
Textual studies
Lecture with practical applications
professional skills
Students' portfolio
Practicum
Task-based study method
general eligibility
Task-based study method
assessment methods
professional knowledge
Test
Oral exam
professional skills
Quality of a written report
Skills demonstration during practicum
general eligibility
Quality of a written report
Recommended literature
  • Dostál Z., Beremlijski P. Metody optimalizace. VŠB-TU Ostrava a ZČU v Plzni, 2012.
  • Lukšan, Ladislav. Metody s proměnnou metrikou : Nepodmíněná minimalizace. 1. vyd. Praha : Academia, 1990. ISBN 80-200-0211-1.
  • Machalová J., Netuka H. Nelineární programování: teorie a metody. Univerzita Palackého v Olomouci, 2013.
  • Machalová J., Netuka H. Numerické metody nepodmín?né optimalizace. Univerzita Palackého v Olomouci, 2013.
  • Nocedal J., Wright S. Numerical Optimization, Second edition. Springer Verlag, 2006.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Applied Physics and Physical Engineering (2015) Special and interdisciplinary fields 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Winter
Faculty of Applied Sciences Applied Physics and Physical Engineering (2017) Special and interdisciplinary fields 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2014) Economy 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 3 Winter
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2014) Economy 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2014) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2011) Economy 1 Winter
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 3 Winter