A Numerical Technique for Solving Optimization Problems

Abstract

The aim of this paper is to calculate a better approximation value (whether it is maximize or minimize ) for one- and two-dimensional nonlinear equations using the best numerical optimization algorithms, which is Newton's method. The idea of this technique is based on approximating the function by expanding the Taylor series expansion and iteratively updating the estimate of the optimal solution. we have obtained good results in terms of accuracy and speed of approach, as shown in the examples mentioned. We also mentioned the applications of Newton’s method in multiple disciplines, including engineering, physics, economics, finance, computer graphics, machine learning, image processing, and other applications.