MU24006 Optimization Methods in Practice

Mathematical Institute in Opava
Winter 2021
Extent and Intensity
2/1/0. 6 credit(s). Type of Completion: zk (examination).
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
Mon 13:05–14:40 20
  • Timetable of Seminar Groups:
MU24006/01: Mon 14:45–15:30 20, K. Hasík
Prerequisites (in Czech)
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
Course objectives (in Czech)
Student dokáže využít teoretických znalostí optimalizačních metod k vyřešení praktického problému, který zpracuje formou projektu.
  • 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.

    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
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.
ActivityDifficulty [h]
Domácí příprava na výuku44
Příprava na zápočet16
Příprava na zkoušku16
Semestrální práce50
The course is also listed under the following terms Winter 2009, Winter 2010, Winter 2011, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019.
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