Nonlinear Programming Techniques in Optimization: An exhaustive comparative study understanding Quasi – Newton and Gauss – Newton methods

Abstract

Non – linear Programming Applications are becoming increasingly important as managers and operations researchers become more sophisticated in implementing decision – oriented mathematical models, as well as computer routines capable of solving large – scale nonlinear problems become more widely available. By means of this paper, we investigate two of the very widely and varied NLP techniques, namely the Gauss – Newton method and the Quasi – Newton method. When computation or iteration is expensive, Quasi –Newton methods are an effective method for function optimization. Even if their precise approaches differ, when the issues are complicated, they can all determine the optimum more quickly and effectively than Newton's Method. Gauss – Newton can be used to locate a single point or, as it is most frequently use, to evaluate how well a theoretical model matches a collection of experimental data points. We get the most accurate estimates of the unknown variables in a theoretical model by solving the system of nonlinear equations. In this review we present an overview of the methods mentioned earlier, discuss the scope of them, and advocate a comparison between the two.