Proširena Lagrangeova metoda

master's thesis

• Title (english): Augmented Lagrange method
• Author: Krešimir Rudec
• Mentor: Marko Vrdoljak (mentor)
• Committee member: Marko Vrdoljak (predsjednik povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-03-03, 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: pojam kaznene funkcije; Lagrangeovi množitelji; uvjetna minimizacija
• Keywords (english): penalty function; Lagrange multipliers; constrained minimization problem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:231782
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-03-30 11:39:54