You had some typos in your constrain function and also you don't need to create a function file for your function since you already use an annonymous one. Use this and it should work:
f = @(x) (x(1) - 2).^2 + (x(2) - 4);
x0 = [1,1]; % Here you put your x0 function you said you had
nonlcon = @mycon;
x = fmincon(f,x0,[],[],[],[],[],[],nonlcon)
% Another file
function [ c,cequ ] = mycon( x )
c=[-x(1);
-x(2);
2*x(1).^2+x(2).^2-34;
2*x(1)+3*x(2).^2-18]; %% I'm not sure if this is even written correctly.
cequ=[];
end
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
<stopping criteria details>
x =
2.0000 0.0000
