Newton based homotopy optimization method for solving global optimization problem

Abstract

Optimization method is widely used in mechanics and engineering, economics, operations research and engineering controls. Various methods have been introduced to solve the optimization problem and mostly it will get a local optimum. One of the most commonly used method is the Newton-Raphson method. In this method, there are some circumstances where it is unable to solve the optimization problem. With the help of homotopy, the problems faced by the Newton-Raphson method can be overcome and thus solve the optimization problem. Therefore, the aim of this study is to investigate the Newton-Raphson method as the basis for the homotopy optimization method for finding local minimum and also the global minimum. There are several auxiliary homotopy functions that should be selected and this project using the Newton Homotopy and Fixed-Point Homotopy. The ability for these two functions are compared in solving optimization. To strengthen these findings, the project is programmed using MATLAB to implement the Newton’s based Homotopy Optimization Method. The four functions of univariate and multivariate are provided for illustrative purposes. This project has succeeded to compare the ability of these two auxiliary homotopy functions in solving global optimization method.