梯度下降不能收敛到功能的最小值

Question

我尝试使用梯度下降来找到函数的局部最小值，Im使用具有动量的梯度下降，但是它只会收敛到我期望的局部最小值附近的点。这是我的梯度下降函数：

Point gradient_descent(double dx, double dy, double error, double gamma, unsigned int max_iters, double moment) {

double cur_error_x = error;
double cur_error_y = error;
double cur_error_moment_x = 0;
double cur_error_moment_y = 0;

unsigned int iters = 0;
double p_error_dx;
double p_error_dy;
double v_x = 0, v_y = 0;
double v_x_pre = 0, v_y_pre = 0;

std::string savePath = "D:\\GradientDescent.csv";

std::ofstream writeFile(savePath);
writeFile << "dx,dy,E(dx;dy)\n";

double dxMin = 1000, dyMin = 1000;
do {
    p_error_dx = dx;
    p_error_dy = dy;

    //NAG
    v_x = moment * v_x_pre + gamma * dfx(p_error_dx - moment * v_x_pre , p_error_dy - moment * v_x_pre);
    v_y = moment * v_y_pre + gamma * dfy(p_error_dx - moment * v_x_pre , p_error_dy - moment * v_x_pre);
    dx -= v_x;
    dy -= v_y;

    cur_error_moment_x = (p_error_dx - dx);
    cur_error_moment_y = (p_error_dy - dy);
    cur_error_x = abs_val(p_error_dx - dx);
    cur_error_y = abs_val(p_error_dy - dy);

    printf("\ni= %i \n", iters);
    printf("\nc_error x= %f\n", cur_error_x);
    printf("\nc_error y= %f\n", cur_error_y);
    printf("\n==================================\n");
    printf("\ndx = %f , dy= %f \n", dx, dy);
    printf("\n E(dx,dy)= %f\n", cost_func(dx, dy));
    printf("\n==================================\n");
    writeFile << dx << "," << dy << "," << cost_func(dx, dy) << std::endl;
    iters++;
    v_x_pre = v_x;
    v_y_pre = v_y;
    if (cost_func(dx, dy) < cost_func(dxMin, dyMin)) {
        dxMin = dx;
        dyMin = dy;
    }
} while ((error < cur_error_x || error < cur_error_y)  && iters < max_iters);

v_x = 0; v_y = 0;
v_x_pre = 0; v_y_pre = 0;

writeFile.close();
return Point(dxMin, dyMin);

}

这是我在云中绘制的结果比较： the function converge near the minimum

it just converge in some point near the minimum