Consider a feasible set $\Omega = \{(x_1,x_2) \in \mathbb{R}^2: -x_2 \leq 0\ and \ x_2-{x_1}^2\leq 0 \} $. For $x^*={(0,0)}^T$. Determine if the tangent cone and linearized feasible solutions are equal.
I am having difficulty in finding the tangent cones. I built sequences $(w_1/k,w_2/k)$, where $w_1 \neq0 \ and \ w_2 \geq0$ and $(w_1/k,{w_1}^2/k^2)$, where $w_1 \in \mathbb{R}$. By definition of tangent cone, I have to find all vectors tangent to $\Omega$ at $x^*$. So I am not sure if I have covered all vectors.