最速下降法matlab程序框图
时间: 2023-11-20 20:54:35 浏览: 143
是最速下降法matlab程序框图的步骤:
```matlab
% 最速下降法matlab程序框图
% 输入:目标函数f,梯度函数g,初始点x0,精度tol
% 输出:最优解x,最优解对应的函数值f(x)
function [x, fval] = steepestDescent(f, g, x0, tol)
% 初始化
x = x0;
fval = f(x);
gval = g(x);
k = 0;
% 迭代
while norm(gval) > tol
% 计算搜索方向
d = -gval;
% 确定步长
alpha = backtracking(f, g, x, d);
% 更新x
x = x + alpha * d;
% 更新fval和gval
fval = f(x);
gval = g(x);
k = k + 1;
end
end
```
其中,backtracking函数是最速下降法中的一种确定步长的方法,其实现如下:
```matlab
% 最速下降法中的backtracking函数
% 输入:目标函数f,梯度函数g,当前点x,搜索方向d
% 输出:步长alpha
function alpha = backtracking(f, g, x, d)
% 初始化
alpha = 1;
rho = 0.5;
c = 0.1;
% 迭代
while f(x + alpha * d) > f(x) + c * alpha * g' * d
alpha = rho * alpha;
end
end
```
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