The purpose of this dissertation was to provide a review of the theory of Optimization, in particular quadratic programming, and the algorithms suitable for solving both convex and non-convex quadratic programming problems. Optimization problems arise in a wide variety of fields and many can be effectively modeled with linear equations. However, there are problems for which linear models are not sufficient thus creating a need for non-linear systems. This dissertation includes a literature study of the formal theory necessary for understanding optimization and an investigation of the algorithms available for solving a special class of the non-linear programming problem, namely the quadratic programming problem. It was not the intention of this dissertation to discuss all possible algorithms for solving the quadratic programming problem, therefore certain algorithms for convex and non-convex quadratic programming problems were selected for a detailed discussion in the dissertation. Some of the algorithms were selected arbitrarily, because limited information was available comparing the efficiency of the various algorithms. Algorithms available for solving general non-linear programming problems were also included and briefly discussed as they can be used to solve quadratic programming problems. A number of algorithms were then selected for evaluation, depending on the frequency of use in practice and the availability of software implementing these algorithms. The evaluation included a theoretical and quantitative comparison of the algorithms. The quantitative results were analyzed and discussed and it was shown that the results supported the theoretical comparison. It was also shown that it is difficult to conclude that one algorithm is better than another as the efficiency of an algorithm greatly depends on the size of the problem, the complexity of an algorithm and many other implementation issues. Optimization problems arise continuously in a wide range of fields and thus create the need for effective methods of solving them. This dissertation provides the fundamental theory necessary for the understanding of optimization problems, with particular reference to quadratic programming problems and the algorithms that solve such problems. Keywords: Quadratic Programming, Quadratic Programming Algorithms, Optimization, Non-linear Programming, Convex, Non-convex.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nmmu/vital:11086 |
| Date | January 2004 |
| Creators | Vankova, Martina |
| Publisher | University of Port Elizabeth, Faculty of Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Masters, MSc |
| Format | 169 pages, pdf |
| Rights | Nelson Mandela Metropolitan University |
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