Extreme ray

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An extreme ray of a closed set LaTeX: S is a ray in LaTeX: S that cannot be expressed as a (simple) sum of other rays in LaTeX: S. For example, the axes, LaTeX: \{t e_j: t \ge 0\}, are extreme rays of the non-negative vectors in LaTeX: \mathbb{R}^n. The ray LaTeX: \{t e: t \ge 0\}, however, is the sum of the axes since LaTeX: (t,...,t) = t e_1 + \ldots + t e_n. The recession direction of an extreme ray is sometimes called an extreme direction.


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