#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<stdio.h>
#include<fstream>
using namespace std;
#define Grad1(x,y) 4*(x-2)*(x-2)*(x-2)+2*(x-2*y) //一阶导
#define Grad2(x,y) -4*(x-2*y) //二阶导
#define Gradf1(x,y) 12*(x-2)*(x-2)+2
#define Gradf2(x,y) 8
//函数f(x,y)=(x-2)^4+(x-2y)^2
int main()
{
double Initx = 0;//初始点x
double Inity = 3;//初始点y
double gradx = Grad1(Initx, Inity);
double grady = Grad2(Initx, Inity);
double twicegradx = Gradf1(Initx, Inity);
double twicegrady = Gradf2(Initx, Inity);
double dx = -gradx / twicegradx;
double dy = -grady / twicegrady;
while (fabs(dx)>1e-10 || fabs(dy)> 1e-10)//epison
{
Initx += dx;
Inity += dy;
gradx = Grad1(Initx, Inity);
grady = Grad2(Initx, Inity);
twicegradx = Gradf1(Initx, Inity);
twicegrady = Gradf2(Initx, Inity);
dx = -gradx / twicegradx;
dy = -grady / twicegrady;
}
cout << Initx << " " << Inity << endl;
cout << powf(Initx - 2, 4.0) + powf(Initx - 2 * Inity, 2.0) << endl;
system("pause");
return 0;
}
Newton's method to find the extreme value of convex function
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Origin blog.csdn.net/yoonaanna/article/details/128987585
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