Sum of functions created by loop for minimization

I have a cell 4x4 of functions of activation energy E named s. I am attempting to make a function of sum of all of the elements to be subject to minimization by function 'fminunc'. But it appears all sum Matlab functions need values, not functions as input so I run to errors. Could you please help with some nice command? Thanks.

p.s.

I'm trying to avoid creating additional function files.

fun = @(T)exp((-E/R)./T);
%for i=1:no_alphas
%Ti = T_sets(i,:);
Ti = [350 400 450 500];
%see function activation min
for j=1:no_rates
 for k=1:no_rates
   if j~=k
    % creates a cell array n x n of all functions
    part = @(E)(integral(fun,Tmin,Ti(j))*(beta(k)))/(integral(fun,Tmin,Ti(k))*beta(j));
    s{j,k} = @(E)(integral(fun,Tmin,Ti(j))*(beta(k)))/(integral(fun,Tmin,Ti(k))*beta(j)); % cell 4x4 of functions 
    
    summm = @(E)(summm(E) + part(E)) % sum of functions not working
    
    %cumsum(s) % does not work
    end
 end
end
[E0,fval] = fminunc(summm,70e3)

[Matt J]

Is E a scalar? If so fminunc seems like overkill. You could just as well use fminsearch.

[Martin Privara]

E should be a scalar after it is found by minimization

Answer 1

[Matt J]

I'm trying to avoid creating additional function files.

Then why not an anonymous function or a local function, e.g.,

function [E0,fval] = myOptimization

 R=...
 T=...
 Tmin=...
 beta=...
 Ti = [350 400 450 500];

 [E0,fval] = fminunc(@summm,70e3)

    function out=summm(E) %Anonymous
        
        fun = @(T)exp((-E/R)./T);
        
        I=Ti; %pre-allocate
        for n=1:numel(I)
         I(n)=integral(fun ,Tmin,Ti(n))*beta(n);
        end
        
        parts=I./I(:);
        parts(1:n+1:end)=0; %exclude j==k
        
        out=sum(parts(:));

    end

end

[Martin Privara]

Thank you for your answer. When I make a local function inside my script I get this error message:

Error: File: Martin_script_new10.m Line: 271 Column: 1
Function definitions in a script must appear at the end of the file.
Move all statements after the "myOptimization" function definition to before the first local function definition.

[Martin Privara]

I'm trying the new version you just uploaded but I'm getting an error because E is not defined. Regardless, I've solved it using another function file in similar way like you are suggesting yesterday.

[Matt J]

Don’t run your optimization in a script. Make it it’s own function file. Or, take the advice of the error message and move function definitions to appropriate locations.