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master's thesis
Proširena Lagrangeova metoda
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:231782
Rudec, Krešimir
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Rudec, K. (2022). Proširena Lagrangeova metoda (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:231782

Rudec, Krešimir. "Proširena Lagrangeova metoda." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:231782

Rudec, Krešimir. "Proširena Lagrangeova metoda." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:231782

Rudec, K. (2022). 'Proširena Lagrangeova metoda', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:231782

Rudec K. Proširena Lagrangeova metoda [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:231782

K. Rudec, "Proširena Lagrangeova metoda", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:231782

Metadata
TitleProširena Lagrangeova metoda
Title (english)Augmented Lagrange method
AuthorKrešimir Rudec
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberPavle Pandžić (član povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-03-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U radu se proučava proširena Lagrangeova funkcija. Za zadaće minimizacije uz uvjete tipa nejednakosti i jednakosti uvodi se pojam kaznene funkcije. Dokazuju se osnovni teoremi o svođenju zadaće uvjetne minimizacije metodom kaznene funkcije na zadaću bezuvjetne minimizacije. Proširena Lagrangeova funkcija se predstavlja u vidu kaznene funkcije. Ustanovljuje se veza bezuvjetne minimizacije ove funkcije s klasičnim rezultatom o Lagrangeovim množiteljima. Prikazana je i praktična primjena proširene Lagrangeove funkcije u numeričkom rješavanju zadaće uvjetne minimizacije.
Abstract (english)
The thesis studies the augmented Lagrange function. For minimization problems with presence of equality and inequality constraints the concept of penalty function is introduced. The basic results on the reduction of constrained minimization problem to the unconditional minimization problem by the method of penalty function are proved. The augmented Lagrangian function is represented as a penalty function. The relation of the unconstrained minimization of this function with the classical results on Lagrange multipliers is established. The practical application of the augmented Lagrangian function for the numerical solution of the constrained minimization problem is also presented.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:231782
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-03-30 11:39:54