| Title | Linearno programiranje |
| Author | Petra Višić |
| Mentor(s) | Snježana Braić (thesis advisor)
|
| Abstract | Ovaj rad obrađuje teoriju linearnog programiranja. Na početku je izložena potrebna teorija iz područja linearne algebre: vektorski prostori s posebnim naglaskom na Euklidski prostor Rn, sustavi linearnih jednadžbi i nejednadžbi te traženje njihovih (bazičnih) rješenja. Središnji je dio posvećen samoj definiciji problema linearnog programiranja (u općem, standardnom i kanonskom obliku), pojmu dualnosti i nizu uz to vezanih teorema o egzistenciji (optimalnog) rješenja. Slijede osnove teorije konveksnih skupova i intuitivna grafička metoda. Naposljetku, opisana je najpoznatija metoda rješavanja problema linearnog programiranja - simpleks metoda. Obje su metode ilustrirane odgovarajućim primjerima. |
| Keywords | optimization Euclidean space basic solution Gauss-Jordan elimination replacement operation objective function linear constraint duality graphical method simplex method |
| Parallel title (English) | Linear programming |
| Committee Members | Snježana Braić (committee chairperson)
Milica Klaričić Bakula (committee member)
Ivan Jelić (committee member)
|
| Granter | University of Split
University of Split, Faculty of science |
| Lower level organizational units | Department of Mathematics |
| Place | Split |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching |
| Study specialization | major in computing |
| Academic title abbreviation | mag. math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2018-01-15 |
| Parallel abstract (English) | This thesis studies the theory of linear programming. The first part gives insight into necessary linear algebra theory: vector spaces (especially Euclidean space Rn), systems of linear equations and inequalities and their solving method. The central part focuses on definition of linear program (in standard, canonical and general form), concept of duality and (optimal) so lution existence theorems. The thesis then presents the basics of convex set theory necessary for following intuitive graphical method. Finally, the best known method for solving linear problems, the simplex method, is demonstra ted. The linear programming solving methods are illustrated with appropriate examples. |
| Parallel keywords (Croatian) | optimizacija Euklidski prostor bazično rješenje Gauss-Jordanove formule eliminacija operacija zamjene funkcija cilja linearno ograničenje dualnost grafička metoda simpleks metoda |
| Resource type | text |
| Access condition | Access restricted to students and staff of home institution |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:166:508670 |
