Minimizing a multivariable function

Hello, i am trying to find the minimum of a multivariable function (the number of variables may vary also but there is a pattern to construct the function) the code i am running is the following:

function F = jac(x)
n=input('n=');
x0=random('unid',90,1,n,1);
x0=pi./x0;
E=input('E=');
h=3;
F=0;
for i=1:n
    D= 0.5;
%     V=0;
%     b=0;
    for j=1:n
        if (mod(j,2)==0)
           D = D + cos(h*x(j));
        else
           D = D - cos(h*x(j)); 
        end 
    end
    D=(2*E*sqrt(2)/(pi*h))*abs(D);
    F = F + 1/h*(D^2);
    h=h+2;
end
M=fminsearch(@(x)jac,x0);

the error i am getting is that the function x is undefined can anyone help me please? thanks in advance

[John D'Errico]

Please learn to format your code to make it readable. I did it for you this time. (Look for the code button.)

[John D'Errico]

Now that I can read your code, I see the call to random. random functions are quite difficult to minimize. However, it looks like you think that is a call to create starting values.

Worse, you have several input statements in the beginning of the function you are trying to minimize? WHY????

My guess from all these things (and others in your code) is you don't have a clue how an optimizer works or how to call one. Or maybe you don't understand how to write functions. It looks like you are confused about what the objective function called by an optimizer should be doing.

Time to start reading the help. Look at the examples. Then and only then, try solving a SMALL optimization problem where you know the answer. Work up to real world problems only when you understand how to solve basic ones.

Answer 1

[Star Strider]

You are going to encounter the recursion error when you run your code because you seem to be calling fminsearch inside your function.

I didn’t run your code however certain parts of it need to be corrected.

Define your ‘n’ and ‘E’ variables outside the function in your workspace and pass them as arguments. Redefine your function statement to accommodate them.

For example, the function statement becomes:

 function F = jac(x,n,E)

then eliminate the input statements inside ‘jac’. Your script then becomes:

x0=random('unid',90,1,n,1);
x0=pi./x0;
n = ...    % <— Define ‘n’
E = ...    % <— Define ‘E’
M=fminsearch(@(x)jac(x,n,E),x0);

Your function becomes:

function F = jac(x,n,E)

h=3;
F=0;
for i=1:n
    D= 0.5;
%     V=0;
%     b=0;
    for j=1:n
        if (mod(j,2)==0)
           D = D + cos(h*x(j));
        else
           D = D - cos(h*x(j)); 
        end 
    end
    D=(2*E*sqrt(2)/(pi*h))*abs(D);
    F = F + 1/h*(D^2);
    h=h+2;
end

end

These changes should get you started. Again, I didn’t run this because it’s not obvious to me what you want to do.

[Physiker192]

okay that is what i tried to do previousely but i had a problem which is that everytime i enter the value of E the program has done nothing but asking me to enter it again and again (but i didn't define the function as f(x,n,E)) i will try it now

[Physiker192]

thank you very much it works. I believe that my mistake was not defining f as a function of (x,n,E) the last code that i posted was an attempt to deal with it as a single file so it wouldn't ask me repetevely to enter E. Anyway thanks a lot.

[Star Strider]

My pleasure!