proper cone
A proper cone is a cone (http://planetmath.org/Cone3) $C\subset {\mathbb{R}}^{n}$ that satisfies the following:

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$C$ is convex;

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$C$ is closed;

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$C$ is solid, meaning it has nonempty interior;

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$C$ is pointed, meaning $x,x\in C\Rightarrow x=0$.
A proper cone $C$ induces a partial ordering on ${\mathbb{R}}^{n}$:
$$a\u2aafb\iff ba\in C.$$ 
This ordering has many nice properties, such as transitivity, reflexivity^{}, and antisymmetry.
References
 1 S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
Title  proper cone 

Canonical name  ProperCone 
Date of creation  20130322 14:37:13 
Last modified on  20130322 14:37:13 
Owner  dooder0001 (4288) 
Last modified by  dooder0001 (4288) 
Numerical id  7 
Author  dooder0001 (4288) 
Entry type  Definition 
Classification  msc 52A20 
Related topic  Cone3 
Related topic  Cone5 