MU:MU24006 Optimization Methods in Pract. - Course Information

MU24006 Optimization Methods in Practice

Extent and Intensity

2/1/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Karel Hasík, Ph.D. (lecturer)
RNDr. Petra Nábělková, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava

Timetable

Mon 13:05–14:40 20

• Timetable of Seminar Groups:

MU24006/01: Mon 14:45–15:30 20, K. Hasík

Prerequisites (in Czech)

TYP_STUDIA(N)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Mathematical Modelling (programme MU, NMgr-M)

Course objectives (in Czech)

Student dokáže využít teoretických znalostí optimalizačních metod k vyřešení praktického problému, který zpracuje formou projektu.

Syllabus

• 1. Introduction: Modeling and optimization. Types of problems and methods, examples. Assignment of semester projects.
  2. Extrema of functions of one varriable. Fibonacci method and golden section search. Secant method. Newton's method.
  3. Optimization without constraints:
  gradient methods, Newton's method and its variants, the method of the conjugate gradient, quasi-Newton methods, comparative methods.
  4. Optimization with constraints:
  Nonconvex and convex problems, method of Lagrange multipliers and generaliizations, penalization and barrier methods, method of projection and reduction of the gradient.
  5. Linear, quadratic, and nonlinear programming. Linear problems with special structure. Duality.
  6. Further practical methods: Stochastic methods, genetic algorithms, discrete methods.
  
  
  

Literature

required literature
• V. M. Alexejev, S. V. Fomin, V. M. Tichomirov. Matematická teorie optimálních procesů. Academia, Praha, 1991. ISBN 80-200-0319-3. info
• P. E. Gill, W. Murray, M. H. Wright. Practical optimalization. Academic Press, London and New York, 1981. info

not specified
• M. Maňas. Optimalizační metody. SNTL, Praha, 1991. info

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course can also be completed outside the examination period.

Teacher's information

Requirements for obtaining the credit:
- Self-study of any mathematical model from any area.
- Developing the project in the specified scope, form and deadline.
- Successful defense of the project in the form of a presentation.

Activity	Difficulty [h]
Cvičení	10
Domácí příprava na výuku	44
Přednáška	20
Příprava na zápočet	16
Příprava na zkoušku	16
Semestrální práce	50
Summary	156

• Enrolment Statistics (Winter 2021, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2021/MU24006