Recession cone

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(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 \}.


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