Metode direktnog traženja u problemima bezuvjetne minimizacije

undergraduate thesis

• Title (english): Direct search methods in unconstrained minimization problems
• Author: Miro Harbaš
• Mentor: Josipa Pina Milišić (mentor)
• Committee member: Josipa Pina Milišić (predsjednik povjerenstva)
• Committee member: Mario Krnić (član povjerenstva)
• Committee member: Anamari Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2020-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu opisan je problem bezuvjetne minimizacije, a zatim je dana apstraktna definicija metoda pretraživanja uzoraka i od čega su te metode sastavljene.
Tom karakterizacijom dan je pregled svojstva globalne konvergencije za takve metode koja ne nameće dovoljno smanjenje koraka.
Dan je pregled standardnih metoda direktnog pretraživanja: Nelder-Mead simpleks algoritma, Hooke-Jeeves algoritma te metoda višesmjernog traženja.
Ujedno je dan je grafički prikaz djelovanja istih algoritama.
Na kraju dan je vizualni prikaz rada metoda pretraživanja uzoraka na primjer uspona na planinu Mount Washington uz pomoć alata Matlab Global Optimization Toolbox.

Abstract (english)

In this paper the problem of unconstrained minimization is defined before giving an abstract definition of pattern search methods and their components.
This characterization is then exploited to establish a global convergence theory that does not enforce a notion of sufficient decrease.
After that, an overview of the Nelder-Mead simplex algorithm, Hooke-Jeeves algorithm and multidirectional search is given along with a graphical representation of the respective algorithms.
Finally, on an example of climbing Mount Washington a visual presentation of how pattern search optimizes an objective function is shown using the Matlab Global Optimization Toolbox.

• Keywords: bezuvjetna numerička optimizacija; metode direktnog traženja; analiza konvergencije
• Keywords (english): unconstrained numerical optimization; direct search methods; convergence analysis
• Language: croatian
• URN:NBN: urn:nbn:hr:168:961262
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-14 20:32:54