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Course, academic year 2018/2019
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Selected Topics on Optimisation Theory and Methods I - NOPT006
Title in English: Vybrané partie z teorie a metod optimalizace I
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2012 to 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Karel Zimmermann, DrSc.
Class: Informatika Mgr. - volitelný
Classification: Informatics > Optimalization
Annotation -
Last update: G_I (26.10.2001)
A survey of basic theory and methods of optimization: necessary theoretical background of linear algebra,linear programming, convex programming, solution methods for general problems and for selected problems with a special structure.Continuation in the next term with the second part of the lecture is assumed.
Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

Karmanov,V.G.: Matěmatičeskoje programmirovanije, Moskva \"Nauka\" 1986

Poljak,B.T.:Vvěděnije v optimalizaciju, Moskva \"Nauka\" 1983

Rockafellar,R.T.: Convex Analysis, Princeton University Press 197O, rus. překlad z r. 1973 vydalo nakl. \"Mir\" Moskva

Hamala,M.: Nelineárne programovanie,2.vyd.,Alfa Bratislava

Himmelblau,D.M.: Applied Nonlinear Programming,McGraw-Hill 1972,rus.překlad vzd. nakl. \"Mir\" Moskva 1975

Ašmanov,S.A.,Timochov,A.V.: Těorija optimizacii v zadačach i upražněnijach, Moskva \"Nauka\", 1991

Syllabus -
Last update: T_KAM (20.04.2007)

1. Basic properties of convex sets.

2. Basic properties of convex functions.

3. Convex optimization, Kuhn-Tucker theory.

4. Some generalizations, quasi-convex and pseudo- convex functions.

5. Non-differentiable convex functions, subgradients.

6. Minimization of functions of one variable.

7. Quadratic optimization.

8. Methods of feasible direction.

9. Gradient methods.

10. Sequential unconstrained minimization techniques, penalty and barrier


11. Some method of discrete optimization.

12. Selected approaches to multi-criterion optimization problems.

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