Matlab code, one-dimensional search and retreat method to determine the search interval

In the use of two-dimensional optimization algorithm, it is often necessary to call one-dimensional search algorithm to find the step, while one-dimensional search algorithm needs to determine the search interval. The method can not only be used as a one-dimensional search algorithm, but also can be used to determine the one-dimensional searching interval.

The principle of the search interval determined by the Retreat method is:

Suppose the one-dimensional objective function is a single-peak function, the initial point x0, the step h, and the iteration point x1= x0+h. The Lamda initial value is set to 1.

(1) if f (x0) > F (x1), then x2=x1+lamda*h. Find a Lamda, make F (x2) > F (x1), Output search interval [x1, X2].

(2) if f (x0) <= F (x1), then x2=x1-lamda*h. Find a Lamda, make F (x2) > F (x0), output search interval [x2, x0].

Individuals think only to determine the search interval, the step value will not be reduced, has been enlarged. The MATLAB code is as follows:

function [LOW,UP]=MINJT (fun,x0,h)
% fun is an anonymous function

lamda=1;
X1=x0;x2=x0+h;

If Fun (x1) >fun (x2)
    x_panduan=x2;
    While 1
        x1=x2;x2=x1+lamda*h;
        Lamda=1.1*lamda;
        If Fun (x2) >fun (X_panduan) break
            ;
        End
    End
else
    x_panduan=x1;
    While 1
        x1=x2;x2=x1-lamda*h;
        Lamda=1.1*lamda;
        If Fun (x2) >fun (X_panduan) break
            ;
        End
    End
End

low=min (X_PANDUAN,X2);
Up=max (X_PANDUAN,X2);

End

For example:

[Low,up]=minjt (@ (x) x^4-x^2-2*x-5,0,0.1)

Output:

Low =
0.1000

up =
1.6937