Fréchet normal cone
= Fréchet normal cone
{c}
{title2=$\widehat N_C(z)$}
= Regular normal cone
{synonym}
A vector $w$ is a regular normal at $z\in C$ when $\limsup_{z^\prime\to z,\ z^\prime\in C\setminus\{z\}}\langle w,z^\prime-z\rangle/\|z^\prime-z\|\leq0$. At an isolated point all vectors satisfy this condition. It is the local first-order supporting cone.