Optimalno upravljanje i primjene u ekonomiji

master's thesis

• Title (english): Optimal management and applications in economics
• Author: Filip Feješ
• Mentor: Marko Erceg (mentor)
• Committee member: Marko Erceg (predsjednik povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-03-01, 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: Mangasarianov teorem; Hamiltonian; maksimizacija profita; Cobb-Douglas; Pontrjaginov princip maksimuma
• Keywords (english): Mangasarian theorem; Hamiltonian; maximizing profit; Cobb-Douglas; Pontryagin maximum principle
• Language: croatian
• URN:NBN: urn:nbn:hr:217:114850
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-13 09:35:07