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master's thesis
Penalty methods in constrained optimization
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:336877
Mihalj, Lucija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mihalj, L. (2019). Penalty methods in constrained optimization (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:336877

Mihalj, Lucija. "Penalty methods in constrained optimization." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:336877

Mihalj, Lucija. "Penalty methods in constrained optimization." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:336877

Mihalj, L. (2019). 'Penalty methods in constrained optimization', Master's thesis, University of Zagreb, Faculty of Science, accessed 16 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:336877

Mihalj L. Penalty methods in constrained optimization [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 May 16] Available at: https://urn.nsk.hr/urn:nbn:hr:217:336877

L. Mihalj, "Penalty methods in constrained optimization", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:336877

Metadata
TitlePenalty methods in constrained optimization
AuthorLucija Mihalj
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
Committee memberGoran Radunović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
This master thesis deals with penalty methods in constrained optimization. The approach is used to convert a constrained problem into an equivalent unconstrained problem. At the beginning, the most important definitions and results related to unconstrained, as well as constrained, optimization are presented. In the second chapter we begin with the basic definition of penalty function. Furthermore, the concept of the penalty function is elaborated and geometrically illustrated. In the next chapter, important result which justifies the use of the penalty function is stated and proven. Also, computational difficulties which motivate the next chapter are discussed. In the fourth chapter, exact penalty functions are presented. Finally, in the last chapter all the methods presented are applied on examples. Firstly, a simple convex optimization problem is solved by all of the methods and results are discussed. After that, cardinality constrained portfolio optimization problem is presented and solved with GUROBI and exterior penalty function method.
Abstract (croatian)
Ovaj rad bavi se s metodom kaznenih funkcija u uvjetnoj optimizaciji koja se koristi kako bi se problem uvjetne optimizacije ekvivalentno zapisao kao problem bezuvjetne optimizacije. Na početku rada navedene su najvažnije definicije i rezultati o bezuvjetnoj, kao i uvjetnoj, optimizaciji. U drugom poglavlju počinjemo s osnovnim definicijama o kaznenim funkcijama. Nadalje, prikazan je koncept kaznenih funkcija i njihova geometrijska interpretacija. U sljedećem poglavlju, naveden je i dokazan rezultat koji opravdava korištenje kaznenih funkcija u uvjetnoj optimizaciji. Također, opisane su računske složenosti koje su motivirale sljedeće poglavlje. U četvrtom poglavlju predstavljene su egzaktne kaznene funkcije. Na kraju rada nalazi se primjena opisanih metoda na jednostavnom konveksnom primjeru. Nakon toga, predstavljen je problem optimizacije portfelja s uvjetom kardinalnosti i riješen je pomoću GUROBI-ja i kaznene funkcije te su dobiveni rezultati uspoređeni.
Keywords
Keywords (english)
Languageenglish
URN:NBNurn:nbn:hr:217:336877
Study programmeTitle: Mathematical Statistics
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 on2020-07-10 10:15:45