cone is used to define the constraint \(\left \lvert x \right\rvert_2 \leq y\) without invoking the overhead of using the norm operator.
c = cone(x,y)
Constraining the Euclidean norm of a vector to be less than 1 is done with
x = sdpvar(n,1); F = cone(x,1);
An alternative form is
F = cone([1;x]);
Of course, arbitrary complicated constructs are possible, such as constraining the norm of the diagonal to be less than the sum of the off-diagonal terms in a matrix.
x = sdpvar(n,n); F = cone(diag(x),sum(sum(x-diag(diag(x)))))
An alternative is to use the norm operator instead (see the examples on nonlinear operators for details)
x = sdpvar(n,n); F = norm(diag(x)) <= sum(sum(x-diag(diag(x))))
The benefit of using the cone command is that the overhead in YALMIP is reduced (no convexity analysis is required).
The operator can be used in a vectorized form. The following model
x = sdpvar(n,1); y = sdpvar(n,1); F = [cone(x,1), cone(y,2)]
is equivalent to
x = sdpvar(n,1); y = sdpvar(n,1); F = [cone([1 2; x y])]