Passing multiple function handles to fminimax

Hey!

I am using fminimax to optimize an arbitrary number of functions that all depend on the same variable, e.g., x. I have a cell array of function handles called Funs, e.g., {@(x)f(x)} {@(x)g(x)}. If I pass this cell array to fminimax as follows:

L = fminimax(Funs, x0, [],[],[],[],LB,UB,[],options),

where x0 is a vector of starting values and LB and UB the lower and upper bounds, respectively, fminimax optimizes only the first function, i.e., f(x).

Now, Let's say I have two function handles and I concatenate the functions into a vector like this

f = Funs{1};

g = Funs{2};

vecFun = @(x)[a(x);b(x)];

and then call fminimax, it correctly optimizes both functions.

My question therefore is, how can I directly call the fminimax with an arbitrary number of functions by using my cell array of function handles? I guess it's just a matter of finding the syntax to convert the cell array into vector function, but I can't quite get it right.

Answer 1

[Rik]

You will have to create a wrapper that calls the functions in your cell array and returns the result as a vector.

Something like the code below should do it (written on mobile, so some edits might be required).

vecFun = @(x)myfun(x,funs);
function val=myfun(x,funs)
val=cellfun(@(f)feval(f,x),funs);
end

[John Rönn]

Hey, thank you very much! I still get the following error code when I run the fminimax function:

FMINIMAX requires all values returned by functions to be of data type double.

[Rik]

Then you need to make sure your functions return a double. Cellfun should not change the datatype. How did you try to confirm that assumption?

[John Rönn]

Hey, I think the problem is that when I try to evaluate my vecFun now with e.g., x0, I get a cell array, let's say 1x2 (with 2 functions). This cell array contains the output values (double) of both functions.However, fminimax does not accept this cell array as the input.

[John Rönn]

% An example code here: 
a = @(x)x;
b = @(x)x.^2;
c = @(x)x.^3;
x0 = 1;
LB = 0;
UB = 1;
Funs = {a,b,c};

vecFun = @(x) cellfun(@(f) f(x), Funs,'UniformOutput',false);
L = fminimax(vecFun, x0, [],[],[],[],LB,UB,[]);

[Walter Roberson]

The function you pass to fminmax cannot return a cell. It must return a numeric vector the same size as your x0, and the result must be the function evaluated at the locations passed in. In other words, it must be vectorized.

fminmax cannot be used to optimize several functions simultaneously.