Matlab: fmincon and inequality constraints (implementation issue) - matlab

Question

I'm working on an optimization problem in Matlab, but unfortunately, I'm stuck.
I want to maximize \theta using the function fmincon, but this particular problem depends on $n$, and $n$ can get very large. There are $n-1$ inequality constraints, all defined with the relation:
For all i \neq j \leq n : \theta - (x_i - x_j)^2 - (y_i - y_j)^2 \leq 0.
So $c(x)$ is an (n-1)x1 - vector.
I'm looking for a way to implement this, so that I don't have to write a new matlab file for each different $n$. (and as you can imagine, when n gets large, that would be one heck of a job)
Any help would be dearly appreciated.
Cheers!
EDIT : I now have created an extra m.file, just for this constraint:
function constraint(n)
%this is a function which creates the constraints of the distance.
for i= 1: n
for j= 1:n
if j==i
continue;
end
(x(i)-x(j))^2 + (y(i)-y(j))^2;
end
end
But the problem now is that matlab goes over the elements one by one. For example: it doesn't calculate (x(1) - x(4))^2 + (y(1) - y(4))^2.
Any idea on how to solve this one?
Thanks again!

Answer 1

I don't see that your function wouldn't at some point calculate that value (when i = 1 and j = 4). The main issue seems to be that your function doesn't return anything, or take in x. According to this, a constraint function should return two things:
Nonlinear constraint functions must return both c and ceq, the
inequality and equality constraint functions, even if they do not both
exist. Return empty [] for a nonexistent constraint.
So first, we need to make sure our constraints are saved into an output vector, c, that c and an empty ceq are returned, and that our function takes both x and n. There might be prettier ways of doing it but
function [c, ceq] = constraint(x,n)
%this is a function which creates the constraints of the distance.
counter = 1;
for i= 1: n
for j= 1:n
if j==i
continue;
end
c(counter)=(x(i)-x(j))^2 + (y(i)-y(j))^2;
c = c+1;
end
end
ceq = [];
end
Next problem: this function takes two inputs, but nonlcon as an input to fmincon needs to take only one, x. We get around this by wrapping this function in an anonymous function (n needs to be predefined), so in the actual fmincon call you would set it to be something like #(x)constraint(x,n)