457-0904/01 – Methods of Optimalizations (MO)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelpostgraduateRequirementChoice-compulsory
Year1Semesterwinter + summer
Study languageCzech
Year of introduction1992/1993Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+0

Subject aims expressed by acquired skills and competences

Student se naučí klasifikovat základní optimalizační úlohy, bude znát podmínky jejich řešitelnosti, a bude znát a umět použít základní varianty efektivních algoritmů, heuristik a softwaru na jejich řešení.

Teaching methods

Summary

Compulsory literature:

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Úvod do variačního počtu. Lineární prostory, funkcionály a jejich diferenciály (Fréchet, Gateaux). Základy variačního počtu, Eulerova rovnice, diferenciály integrálních funkcionálů. Řešení klasických úloh variačního počtu. Minimalizace bez omezení. Jednorozměrná minimalizace unimodulárních funkcí. Podmínky minima, metody Newtonova typu a jejich modifikace. Gradientní metody, metoda sdružených gradientů. Minimalizace s omezením. Karush-Kuhn-Tuckerovy podmínky optimality. Význam Lagrangeových multiplikátorů. Penalizační a bariérové metody pro minimalizaci s omezením. Metoda přípustných směrů (SLP), metoda aktivních množin. Metoda sdružených gradientů pro řešení úloh s jednoduchým omezením. Dualita. Dualita v konvexním programování. Sedlové body, Uzawův algoritmus a rozšířené Lagrangiány. Lineární programování. Úloha lineárního programování a její interpretace. Konvexní množiny popsané lineárními nerovnostmi, jejich konvexní hranice a extrémní směry. Řešení úloh lineárního programování, simplexová metoda. Další optimalizační úlohy a software. Základní pojmy nehladké optimalizace, subgradienty, podmínky minima. Globální optimalizace, metoda simplexů, "tunelování", genetické algoritmy, simulované žíhání, řízené náhodné prohledávání. Software.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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