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master's thesis
Kvadratno programiranje
2020. urn:nbn:hr:166:051290
Sladović, Sara
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Sladović, S. (2020). Kvadratno programiranje (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:051290

Sladović, Sara. "Kvadratno programiranje." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:051290

Sladović, Sara. "Kvadratno programiranje." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:051290

Sladović, S. (2020). 'Kvadratno programiranje', Master's thesis, University of Split, Faculty of Science, accessed 22 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:051290

Sladović S. Kvadratno programiranje [Master's thesis]. Split: University of Split, Faculty of Science; 2020 [cited 2024 November 22] Available at: https://urn.nsk.hr/urn:nbn:hr:166:051290

S. Sladović, "Kvadratno programiranje", Master's thesis, University of Split, Faculty of Science, Split, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:166:051290

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Metadata
TitleKvadratno programiranje
Title (english)Quadratic Programming
AuthorSara Sladović
MentorMilica Klaričić Bakula (mentor)
Committee memberMilica Klaričić Bakula (predsjednik povjerenstva)
Committee memberJurica Perić (član povjerenstva)
Committee memberAljoša Šubašić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2020-09-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu govorimo što je to kvadratno programiranje, formuliramo problem i iskazujemo neka svojstva teorije uvjetne optimizacije. Proučavamo probleme kvadratnog programiranja s jednakosnim i nejednakosnim uvjetima i za obe klase iskazujemo koja su svojstva i optimalni uvjeti. Kod problema s jednakosnim uvjetima rješavamo KKT sustav primjenom par metoda, kao što su simetrično-indefinitna faktorizacija, metoda Schurovog komplementa i metoda nul-prostora. Metode koje opisujemo za probleme s nejednakosnim uvjetima su metoda osnovnog afinog skaliranja za konveksno kvadratno programiranje, osnovna metoda aktivnog skupa za konveksno kvadratno programiranje i metoda projekcije gradijenta. Na samom kraju pokazujemo primjenu kvadratnog programiranja na Markowitzevom modelu optimizacije portfelja i kvadratnom problemu ruksaka.
Abstract (english)
In this thesis, we say what quadratic programming is, and we formulate the problem and express some properties of the constrained optimization. We study the problems of equality and inequality constrained quadratic programming and for both classes we state the properties and optimal conditions. For equality-constrained problems, we solve the KKT system by applying several methods: symmetric indefinite factorization, Schur-complement method and null-space method. For inequality-constrained problems, we describe: the primal affine scaling method for convex quadratic programming, the primal active-set method for convex quadratic programming and the gradient-projection method. At the end, we show the application of quadratic programming on Markowitz portfolio optimization and quadratic knapsack problem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:051290
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2021-02-02 16:40:55