How can I create a handle-function with a double summation on 201 variables (40401 terms)?

Hello everyone!

I have to use Lagrangian multipliers with two linear constrains to minimize the function

where W represent all 201 variables that I want to determine, C are correlation coefficients between two vectors and sigma are standard deviations of the vectors (obviously I have 201 vectors).

To use Lagrangian multipliers, I use the function fmincon.

The problem is that I don't know how create the function .

I think the input function should be a handle-function (and fmincon works with a handle-function), but I don't know how create a so complicated handle funcion.

I used

W = sym('W',[1 201]);

to create my symbolic variables.

Then, I tried to use several methods to create , like

FUN=@(W) symsum(symsum(W('i')*W('j')*S('i','j')*std(L(:,'i'))*std(L(:,'j')), j, 1, 201), i, 1, 201);

When I try to minimize this FUN with fmincon, this error appears:

"Undefined function 'symsum' for input arguments of type 'double'."

Another very complex attempt consists of creating an ausiliar array in which write every term of summations,

FUNau =cell(201*201, 1);
nit=0;
for i=1:201
    for j=1:201
        nit=nit+1;
        FUNau(nit,1) = (W(i)*W(j)*S(i,j)*std(L(:,i))*std(L(:,j)));
        
    end
end

% high computation time

then I tried several methods to compute the right FUN, like

FUN =@(W) sum(FUNau);

or

FUN =@(W) symsum(FUNau);

but every attemp has failed when I used fmincon.

How can I create the function so that fmincon works?

Thanks.

[Torsten]

W and sigma are assumed as column vectors of size 201x1 and C is 201x201.

[Damonyr]

Yes, I've just corrected and that was the point, but now, unfortunately, there is another error:

Error using fmincon (line 609)

Supplied objective function must return a scalar value.

I've already found it yesterday while I was making my attempts and I failed to solve it.

Do you have any idea how to solve it?

[Damonyr]

Ok, I solved it. Thank you so much.

Answer 1

[Torsten]

FUN = @(W) (W.*sigma).'*C*(W.*sigma)

[Damonyr]

Hi Torsten,

Thanks for the reply.

I tried your function, but when I use fmincon this error appears:

"Error using *

Inner matrix dimensions must agree.

Error in @(W)(W.*sigma).'*S*(W.*sigma)

Error in fmincon (line 536)

initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:

Failure in initial objective function evaluation. FMINCON cannot continue."

I thought you forgot a dot after C, but the error persists.

For completeness I write the code for fmincon

lb=zeros(1,201);

ub=ones(1,201);

Aeq=ones(2, 201);

Aeq(2,:)=Gain(1,:);

beq=[1; 0.05];

w0=zeros(1,201);

options = optimoptions('fmincon','Display','off');

[x,fval,exitflag,output,lambda] = fmincon(FUN,w0,[],[],Aeq,beq,lb,ub,[],options);