undergraduate thesis
Nelder - Mead's Method: Local Method for Unconstrained Direct Optimization

Lucijana Grgić (2015)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Zavod za primijenjenu matematiku
Katedra za primijenjenu matematiku
Metadata
TitleNelder - Meadova metoda: Lokalana metoda direktne bezuvjetne optimizacije
AuthorLucijana Grgić
Mentor(s)Kristian Sabo (thesis advisor)
Abstract
Potreba za optimizacijom funkcija čije nam derivacije nisu poznate, 1965.godine dovela je do nastanka Nelder-Meadove metode. U ovome radu je opisana upravo ta metoda, koja se smatra jednom od popularnijih i raširenijih lokalnih metoda direktne bezuvjetne optimizacije. Nelder-Meadova metoda je zanimljiva zbog svoje jednostavnosti sto je pokazano algoritmom u \mathbb{R}^2, kao i generalizacijom u \mathbb{R}^n. Izneseno je nekoliko informacija o konvergenciji ove metode nakon njezinog nastanka, no većinom negativni rezultati pošto dokaz o konvergenciji ove metode ne postoji. Na kraju je prikazan numerički primjer koji potkrijepljuje cijelu priču, kako o jednostavnosti, tako i o nedostacima.
KeywordsNelder-Mead's method Unconstrained optimization Local method Simplex search algorithm
Parallel title (English)Nelder - Mead's Method: Local Method for Unconstrained Direct Optimization
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za primijenjenu matematiku
Katedra za primijenjenu matematiku
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2015-09-18
Parallel abstract (English)
The need to optimize functions whose derivatives are unknown lead to the occurrence of Nelder-Mead's method in 1965. In this work precisely that method is described which is considered one of the most popular and wideused local methods for direct unconstrained optimization. Nelder-Mead's method is interesting because of its simplicity shown by algorithm in \mathbb{R}^2, as the generalization in \mathbb{R}^n. There are several informations about convergence of this method since its apperance, but mostly negative results due to lack of evidence. Finally, a numerical example in this work comrms the whole story, in terms of both simplicity and the disadvantages.
Parallel keywords (Croatian)Nelder-Meadova metoda Bezuvjetna optimizacija Lokalna metoda Simpleks metoda
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:782913
CommitterMirna Šušak Lukačević