Improvements of the Newton–Raphson method

Abstract

The Newton–Raphson (N-R) method is one of the most ubiquitous approaches with several applications in numerous areas to find the optimization solution. It has long been known that in practice to apply the N-R method, it is customarily required to be obtained the second derivative of the objective function. Nevertheless, it is difficult or impossible to find the second derivative of the target function in many situations, leading to the impossibility to obtain the optimization solutions. This paper conducts a numerical method, develops an algorithm, and provides the R code so that one will be able to obtain the optimization solutions when our proposed approach is used. This study investigates numerous simulation studies and a factual data set. Based on the findings in this work, it can be firmly concluded that the N-R method with the numerical method for the second derivative of the objective function is found to be a robust and trustworthy approach.