Solutions of some non-linear programming problems

Abstract

The purpose of this paper was to provide a review of the theory of Optimization, in particular non-linear and quadratic programming, and the algorithms suitable for solving both convex and non-convex programming problems. Optimization problems arise in a wide variety of fields and many can be effectively modelled with linear equations. However, there are problems for which linear models are not sufficient thus creating a need for non-linear systems. This project includes a literature study of the formal theory necessary for understanding optimization and an investigation of the algorithms available for solving of the non-linear programming problem and a special case, namely the quadratic programming problem. It was not the intention of this project to discuss all possible algorithms for solving these programming problem, therefore certain algorithms for solving various programming problems were selected for a detailed discussion in this project. Some of the algorithms were selected arbitrarily, because limited information was available comparing the efficiency of the various algorithms. 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. We discuss the fundamental theory necessary for the understanding of optimization problems, with particular programming problems and the algorithms that solve such problems.