0.618方法matlab流程图,0.618法的matlab实现

以下是0.618方法的Matlab实现的流程图：


以下是0.618方法的Matlab代码实现：

function [fmin,xmin,iter]=golden_section_search(f,a,b,tol)
% f: the objective function
% a, b: the initial interval
% tol: the tolerance level
% fmin: the minimum value of the function
% xmin: the value of the variable at the minimum point
% iter: the number of iterations

% Define the golden ratio
golden_ratio=(1+sqrt(5))/2;

% Calculate the initial values of x1 and x2
x1=b-(b-a)/golden_ratio;
x2=a+(b-a)/golden_ratio;

% Evaluate the function at the initial values of x1 and x2
f1=f(x1);
f2=f(x2);

% Initialize the iteration counter
iter=0;

% Iterate until the desired tolerance level is reached
while abs(b-a)>tol
    iter=iter+1;
    
    % Check which interval is smaller
    if f1<f2
        b=x2;
        x2=x1;
        x1=b-(b-a)/golden_ratio;
        f2=f1;
        f1=f(x1);
    else
        a=x1;
        x1=x2;
        x2=a+(b-a)/golden_ratio;
        f1=f2;
        f2=f(x2);
    end
end

% Return the minimum value of the function and the value of the variable at the minimum point
if f1<f2
    fmin=f1;
    xmin=x1;
else
    fmin=f2;
    xmin=x2;
end
end

该函数的输入参数包括：

- f：目标函数
- a，b：初始区间
- tol：所需的容忍度

该函数的输出参数包括：

- fmin：函数的最小值
- xmin：最小点处的变量值
- iter：迭代次数