# Normal cone

For a convex set $LaTeX: S,$ the normal cone to $LaTeX: S$ at $LaTeX: x,$ for $LaTeX: \textstyle x \in S,$ is $LaTeX: \textstyle \left \{y : \le 0 \mbox{ for all } v \in S \right \},$ where $LaTeX: < * >$ is an inner product.