# Recession cone

(also called characteristic cone), of a given set, $LaTeX: S.$ The set of recession directions for
$LaTeX: \textstyle S: \left \{h: \left \{x+th: t \ge 0 \right \} \in S \mbox{ for some } x \in S \right \}.$
For example, let $LaTeX: rc(S)$ denote the recession cone of S. Then, $LaTeX: \textstyle rc(S)=S$ if $LaTeX: \textstyle S = \mathbb{R}^n$ or if $LaTeX: S=\left \{0 \right \}.$ If
$LaTeX: \textstyle S = \left \{x: Ax \le b \right \}, rc(S) = \left \{h: Ah \le 0 \right \}.$