prikaz prve stranice dokumenta Optimalno upravljanje i primjene u ekonomiji
  Download
PDF 436.81 KB
master's thesis
Optimalno upravljanje i primjene u ekonomiji
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:114850
Feješ, Filip
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Feješ, F. (2024). Optimalno upravljanje i primjene u ekonomiji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:114850

Feješ, Filip. "Optimalno upravljanje i primjene u ekonomiji." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:114850

Feješ, Filip. "Optimalno upravljanje i primjene u ekonomiji." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:114850

Feješ, F. (2024). 'Optimalno upravljanje i primjene u ekonomiji', Master's thesis, University of Zagreb, Faculty of Science, accessed 17 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:114850

Feješ F. Optimalno upravljanje i primjene u ekonomiji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 May 17] Available at: https://urn.nsk.hr/urn:nbn:hr:217:114850

F. Feješ, "Optimalno upravljanje i primjene u ekonomiji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:114850

Metadata
TitleOptimalno upravljanje i primjene u ekonomiji
Title (english)Optimal management and applications in economics
AuthorFilip Feješ
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-03-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ideja ovog rada je upoznati se s teorijom optimalnog upravljanja, matematičkom pozadinom iste i zatim primijeniti pokazane tvrdnje na primjerima iz ekonomije. Izveli smo nužne uvjete za rješenje te pokazali kada će oni biti i dovoljni pomoću Mangasarianovog teorema. Važan alat koji koristimo u svim primjerima je Hamiltonian. Među ostalim, na početku rada uvodimo i dva primjera iz ekonomije koji se protežu cijelim radom: jedan u kojem tražimo optimalan raspored proizvodnje (u smislu minimalnog troška), a drugi vezan uz investiranje s ciljem maksimizacije profita. Za oba prethodno navedena primjera, kao i mnoge druge, s izgradnjom teorije su nađena optimalna rješenja. Za složenije probleme navodimo primjere u kojima imamo dodatne početne uvjete ili neka ograničenja na upravljačku funkciju te probleme više varijabli (Cobb-Douglas). Rad zaključujemo s opće poznatim Pontrjaginovim principom maksimuma.
Abstract (english)
The idea of this thesis is to get acquainted with the theory of optimal control, mathematical background of the same, and then apply the demonstrated statements to examples from economics. We developed the necessary conditions for a solution and showed when they will be both necessary and sufficient with the help of the Mangasarian theorem. An important tool that we used in all examples is the Hamiltonian. At the beginning of the thesis, among others, we introduced two examples from economics that are extended throughout the thesis: one in which we are looking for an optimal production schedule (in terms of minimum cost), and the other related to investing with the aim of maximizing profit. For both of the above examples, like many others, optimal solutions were found when the whole theory was built. For more complex problems, we mentioned examples in which we have additional initial conditions or some other restrictions on control function, and multi-variable problems like Cobb-Douglas. We concluded the thesis with the well-known Pontryagin maximum principle.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:114850
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-03-13 09:35:07