I am new to normal cones. I am trying to compute those two normal cones :
First normal cone
$ C = \{ (u, v) ∈ ( − \infty, 0]^2 : u + v \geq 0 \}$. the normal cone at $(0, 0)$
If I draw $C$ I find the set $\{ u = 0, v \in (- \infty, 0] \}$
I think that the normal cone at $(0,0)$ is the set $\{ u = 0, v \in (0, +\infty] \}$, but I am not sure.
Second normal cone
$C = \{ x \in \mathbb{R}^n, ||x||_2 \leq 1 \}$
I try to compute the normal cone for all $x \in \mathbb{R}^n$.
If $x$ belongs to the interior of $C$, then : $N_C(x) = \{ 0 \}$
If $x$ does not belong to $C$ (such that $||x||_2 > 1$, $N_C(x) = \emptyset$
if $x$ is on the boundary of $C$, I do not manage to find the answer...
Any help ? Please.