Create function handle with several variables/arguments

Hello,

for my master thesis I want to minimize functions of multiple (50+) variables. So far I am doing this by using the function handle commands for an anonymous function. But since I would like to automatically set the right number of terms depending on the current problem, I am wondering, if there is not a better way to do this. What I am doing right now is something like this:

fun = @(z) cv(1)*z(1)+cv(2)*z(2)+cv(3)*z(3)+cv(4)*z(4)+cv(5)*z(5)+cv(6)*z(6)+cv(7)*z(7)+cv(8)*z(8)+...

options = optimoptions(@fmincon,'Display','notify-detailed','Algorithm',algorithm_outside,'MaxFunEvals',50000); %,'ConstraintTolerance',1e6);

startwert = initiations(l,:);
%startwert = Solution(:,3)';
%[mini,min_value] = fmincon(fun,startwert,Aeqb,constraints3,Aeqa,beq,zeros(1,number_of_links),ones(1,number_of_links)*total_demand,[],options);

problem = createOptimProblem('fmincon','objective',fun,'x0',startwert,'Aineq',Aeqb,'bineq',constraints3,'Aeq',Aeqa,'beq',beq,'lb',zeros(1,number_of_links),'ub',ones(1,number_of_links)*total_demand,'options',options);

gs = GlobalSearch;
[mini,min_value] = run(gs,problem);

Obviously, the cv(k) are just some values of type double, that have been calculated before. The same is true for the starting value and the constraints. The variables of the objective fucntion represent links in a traffic network. I would like to be able to tell my script in the beginning that my network has, say n links, and then to automatically have a function handle of the above type with the correct number of variables. What I am doing so far, is that I manually type the number of variables needed, what would amount in an awful lot of work for large networks, potentially in danger of typing mistakes.

Am I right, that this is not working that easily with, for example, a loop?

Thanks in advance for your help!

Regards, David

Answer 1

[Stephen23]

Why not just vectorize the multiplication and summation?:

fun = @(z) sum(cv(:).*z(:));

https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

[David]

Thanks already! Seems to work! I was not aware of this possibility. So telling the function handle z(:) just cuts it at the right amount then? Generally, can I always apply (:) and the size of the vector will be adjusted to the limiting factor (in this case the cv(:))?

And using sum inside the funciton handle is no problem, whereas writing a loop and then saying fun = loop would not work?

[Akshay Yadav]

Are all the variables z(1), z(2), ..., different? I am trying to make a similar function with 50 temperature variables:

for m = 1:50
    f = @(T) sum(A(m,:).*T(:));
    dTdt(m,1) = {f};
end

Where A is a 50x50 coefficient matrix. However, I am only able to evaluate dTdt at only one temperature.

>> dTdt{45,1}(1)

ans =

    0.0012

If try to input multiple variables, it gives the error (like dTdt{45,1}(1,2,1,2,...)) :

Error using Part_2>@(T)sum(A(m,:).*T(:))
Too many input arguments.

Is it possible to evaluate each dTdt at different T(1), T(2), ..., T(50)?