Obtain multiple function handles as outputs from one single function for optimisation.

Hello,

I am in the process of writing a code for an optimisation problem. However, I am stuck with the following problem.

%% Function that generates the cost function and constraint

function [obj_func, constraint]=functiongenerator(a,b,c)
    % parameters a, b and c are passed to this function from anotherscript. They are scalar values
    [obj_func,constraint]=first_func; %% THIS IS THE LINE OF CONCERN %%
    
    function [fun, cons]=first_func(x)
        p=a*x(:,1);
        q=b/c*x(:,2);
        % more computations with p and q
        
        P=[p q p*q];
        Q=[q p p/q];
        
        PQ=Q-P;
        
        fun=@second_func;
        cons=@third_func;
        
        function f=second_func(x)
            f=norm(PQ); %some dummy operation here for representation. The actual operation is a matrix calculation
        end
        
        function ct=third_func(x)
            ct=PQ(2,1); %some dummy operation here for representation. The actual operation is a matrix calculation
        end
        
    end
end

The above code block represents the function file and the following code block represents the script i am running to execute the function file.

a=10;
b=15;
c=20;
[obj_func, constraint]=functiongenerator(a,b,c)

xval = ga(obj_func,2,[],[],[],[],[],[],constraint);

However when I run this code, I get the error that

---not enough input arguments in "THE LINE OF CONCERN"---

The above code is only for representation. My actual problem involves matrix multiplications.

How would I be able to execute my code? Any help is much appreciated.

Thank you

[Stephen23]

You defined FIRST_FUNC with one input argument (required):

function [fun, cons]=first_func(x)

and then call it with zero input arguments (thus the error):

[obj_func,constraint]=first_func;

I presume that x is the array being optimized. In which case returning the function handles is not the problem, the problem is that the code of FIRST_FUNC uses x, but at that point x has not been defined... nor will it be defined until the GA call your functions. So your data-flow is contradictory: if x is that supplied by GA then it cannot be used in code which is called once before you even call GA. Or lets phrase it as a question: given that FIRST_FUNC gets called only once before GA gets called, what value of x do you expect it to have?

As far as I can tell, FIRST_FUNC is superfluous anyway.

[Suhas Raghavendra Kulkarni]

Thank you for that comment Stephen. Your explanation adds the necessary infromation to complete my actual question. The array "x" being used by "first_func" is, like you rightly assumed, the array of variables being optimised.

How would I then be able to formulate this function to address the error?

Answer 1

[Stephen23]

Get rid of FIRST_FUNC.

Move all of the code that depends on x to SECOND_FUNC.

Something like (untested, but should get you started):

function [fun,cons] = functiongenerator(a,b,c)
PQ = []; % ensure that PQ is passed between nested workspaces: "See also" below.
fun  = @second_func;
cons = @third_func;
%
    function f = second_func(x)
        %
        p =   a * x(:,1);
        q = b/c * x(:,2);
        % more computations with p and q
        
        P = [p q p*q];
        Q = [q p p/q];
        
        PQ = Q-P;
        %
        f = norm(PQ); 
    end
%   
    function ct = third_func(x) % what is x used for?
        ct = PQ(2,1);
    end
%
end

See also: https://www.mathworks.com/help/matlab/matlab_prog/nested-functions.html#f4-73993

Note that your THIRD_FUNC does not return two arrays as the GA documentation requires:

https://www.mathworks.com/help/gads/ga.html#d123e45836