牛顿法求凸函数极值

最新推荐文章于 2025-12-20 15:00:56 发布

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#c++

#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;
}