Speed up fminbnd using vectorization

I am trying to optimize this piece of code. I am using the function fminbnd on a vector, splitting the task on its single entries using a loop.

Would it be possible to speed it up vectorizing the process?

        for i = 1:A
            for ii= 1:B
                for iii = 1:C
                    fun = @(x) (x * variable(i,ii,iii))^2 ;
                    [arg_min(i,ii,iii), min_(i,ii,iii)] = fminbnd(fun,0,2);
                end
            end
        end

Thanks for the attention.

Sincerely

Luca

Answer 1

[Matt J]

In your example, the solution is always x=0, so a trivial vectorized solution would be

arg_min=zeros(A,B,C);
min_ = arg_min;

More generally, no, vectorization will not help in a situation like this. You could consider parallelizing the loop using PARFOR.

Answer 2

[Luca Gagliardone]

What if I create a vector x containing all the possible values for minimization:

x = permute(repmat([0:0.01:2]',[1,A,B,C]),[2,3,4,1]);
variable2 = repmat(variable,[1,1,1,length(x)]);
fun = (x .* variable2).^2;
min_ = min(fun,[],4);

That would do an approximation of the above? Thanks.

Luca

Answer 3

[Nick Durkee]

I actually developed a solution to this problem for my research. It's available on the file exchange.

https://www.mathworks.com/matlabcentral/fileexchange/67405-fminbnd-vec-released-funfcn-min-bound-max-bound-num-vecs-