最速下降法matlab全局最小值_利用黄金分割法一维搜索的最速下降法matlab源程序...
时间: 2023-06-24 11:08:30 浏览: 138
以下是最速下降法结合黄金分割法一维搜索的 MATLAB 源代码示例:
```matlab
function [x, fval, k] = steepestDescent(func, x0, tol)
% func: 目标函数句柄
% x0: 初始点
% tol: 迭代停止条件,当梯度的2范数小于该值时停止迭代
% 黄金分割法参数
phi = (sqrt(5) - 1) / 2;
a = 0;
b = 1;
L = b - a;
k = 0;
x = x0;
while norm(gradient(func, x)) > tol
% 计算搜索方向
d = -gradient(func, x);
% 一维搜索
while L > tol
% 计算两个试探点
x1 = a + (1 - phi) * L;
x2 = a + phi * L;
% 计算函数值
f1 = func(x + x1 * d);
f2 = func(x + x2 * d);
% 更新搜索区间
if f1 < f2
b = x2;
else
a = x1;
end
% 更新搜索长度
L = b - a;
end
% 更新当前点
x = x + a * d;
% 更新迭代次数
k = k + 1;
end
% 返回最优解和最优值
fval = func(x);
end
```
其中,`func` 是目标函数的句柄,`x0` 是初始点,`tol` 是迭代停止条件,当梯度的 2 范数小于该值时停止迭代。黄金分割法的参数可以根据具体问题进行调整。最后返回最优解 `x` 和最优值 `fval`,以及迭代次数 `k`。
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