Optimization Problem definition the function

Hi everyone,

I am trying to define a nonlinear optimization function with 3 unknown variables which I need to optimize.

The optimization function is very large and needs a for loop to be defined, furthermore there are no contraint.

But I am having difficulty defining the function within the for-loop, what I currently have is:

syms x1
syms x2
syms x3
table = readtable('data.csv');
array = table2array(table);
x = [x1,x2,x3]';

for i=1:100
    Afun = @(x)((x(1)*array(i,1)-x(2)*array(i,2)+x(3)*array(i,3))^2);
    if i==1
        FUN = Afun;
    else
        FUN = FUN + Afun;
    end
end

But I get an error where the functions do not want to add, generally I am not sure if I am approaching this type of problem correctly with this method.

Any thought? Thanks!

Answer 1

[Dana]

When you do

f = @(x) ...

the variable f isn't a function, but a function handle, i.e., a sort of "pointer" that allows you to refer to the function you've created. As such, it doesn't make sense to add this handle to something.

A better approach to do what it seems you're after is, first of all, do away with the symoblic stuff. You don't need it. Assuming size(array)=[100 3], the following should do what you want:

table = readtable('data.csv');
array = table2array(table);
FUN = @(x) norm(array*x)^2;

Note that the function argument x passed in here should be a 3-element column vector.

[Emma-B]

Thanks so much, it was very helpfull!