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proper cone (Definition)

A proper cone is a cone $ C\subset\mathbb{R}^n$ that satisfies the following:


A proper cone $ C$ induces a partial ordering on $ \mathbb{R}^n$:

$\displaystyle a\preceq b\Leftrightarrow b-a\in C. $
This ordering has many nice properties, such as transitivity, reflexivity, and antisymmetry.


Bibliography

1
S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.



"proper cone" is owned by dooder0001.
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See Also: cone, cone
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Cross-references: antisymmetry, reflexivity, transitivity, properties, partial ordering, induces, interior, solid, closed, convex
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This is version 4 of proper cone, born on 2004-09-20, modified 2004-09-21.
Object id is 6199, canonical name is ProperCone.
Accessed 1942 times total.

Classification:
AMS MSC: 52A20 (Convex and discrete geometry :: General convexity :: Convex sets in $n$ dimensions )
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