Supporting hyperplane
= Supporting hyperplane
{title2=$a^Tx=a^Tx_0$}
For a <convex set> $C$ and $x_0\in C$, a <supporting hyperplane> has a nonzero <normal vector> $a$ such that $a^Tx\le a^Tx_0$ for all $x\in C$. It touches $C$ while containing the set on one side.