Polubeskonačno programiranje

master's thesis

• Author: Dorian Čudina
• Mentor: Marko Vrdoljak (mentor)
• Committee member: Marko Vrdoljak (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Polubeskonačno programiranje je optimizacijski problem u kojem minimiziramo realnu funkciju na konačnodimenzionalnom prostoru, ali uz beskonačno mnogo uvjeta tipa nejednakosti. Ta klasa problema je u ovom radu predstavljena kroz četiri poglavlja u kojima su navedeni važni rezultati iz dualnosti, diskretizacije, uvjeta optimalnosti prvog reda te konvergencije. Posebno su istaknuti slučajevi konveksnog problema i glatkog problema polubeskonačnog programiranja radi njihovih matematički pogodnih... More svojstava. U posljednjem su poglavlju navedene poznate primjene, odnosno načini modeliranja suvremenih problema koji se pojavljuju u robotici, minimizaciji troškova i mjerenju efikasnosti procesa koristeći teoriju polubeskonačnog programiranja. Less

Abstract (english)

Semi-infinite programming is an optimization problem in which a real function is being minimized on a finite-dimensional space, but with infinite number of constrains that must be satisfied, which are represented by inequalities. In this Master thesis, the class of problems is presented through four chapters in which we gave an overview of important results used in solving semi-infinite programming problems, which include results from duality theory, discretization, first order optimality... More conditions and convergence. We emphasized the cases of convex problems and linear problems because of their mathematically nicer properties. In the last chapter, we gave examples of well known problems from areas of robotics, minimizing costs and measuring efficiency of processes that can be solved by modeling them like semi-infinite programming problems. Less

• Keywords: programiranje; optimizacija; konačnodimenzionalni prostor; robotika; minimizacija troškova; mjerenje efikasnosti procesa
• Keywords (english): programming; optimization; finite-dimensional space; robotics; minimizing costs; measuring efficiency of processes
• Language: croatian
• URN:NBN: urn:nbn:hr:217:416251
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-08-23 07:47:44