Convex cones

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(New page: ==Nonorthogonal projection on extreme directons of convex cone== ===pseudo coordinates=== Let <math>\mathcal{K}</math> be a full closed pointed convex cone in some finite dimensional Eucli...)
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Revision as of 20:39, 28 August 2008

Nonorthogonal projection on extreme directons of convex cone

pseudo coordinates

Let $LaTeX: \mathcal{K}$ be a full closed pointed convex cone in some finite dimensional Euclidean space $LaTeX: \mathbb{R}^n$ .

For any vector $LaTeX: \,v\,$ and a point $LaTeX: \,x\!\in\!\mathcal{K}$ , define $LaTeX: \,d_v(x)\,$ to be the largest number $LaTeX: \,t^\star$ such that $LaTeX: \,x-tv\!\in\!\mathcal{K}\,$ .