The Properties of Average Gradient in Local Region

Abstract

This paper studies the average gradient over the local region of a function and constructs the homogenization function of a function. It is found that there are some good properties about the local extreme points and the global extreme points of the function. By using the gradient algorithm, it is more effective to use the homogenization function to find the extreme values of the function. This method implies a method of sifting out the local extreme points of a function.