proper cone

A proper cone is a cone ( Cn that satisfies the following:

  • C is convex;

  • C is closed;

  • C is solid, meaning it has nonempty interior;

  • C is pointed, meaning x,-xCx=0.

A proper cone C induces a partial ordering on n:


This ordering has many nice properties, such as transitivity, reflexivityMathworldPlanetmath, and antisymmetry.


  • 1 S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
Title proper cone
Canonical name ProperCone
Date of creation 2013-03-22 14:37:13
Last modified on 2013-03-22 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