# Euclidean distance cone faces

### From Wikimization

(Difference between revisions)

Line 7: | Line 7: | ||

For a better explanation, see section 6.5.3 in [http://meboo.convexoptimization.com/BOOK/ConeDistanceMatrices.pdf Cone of Distance Matrices]. | For a better explanation, see section 6.5.3 in [http://meboo.convexoptimization.com/BOOK/ConeDistanceMatrices.pdf Cone of Distance Matrices]. | ||

- | Definition of ''exposure'' is in [http://meboo.convexoptimization.com/BOOK/convexgeometry.pdf Convex Geometry]. | + | Definition of ''exposure'' is in [http://meboo.convexoptimization.com/BOOK/convexgeometry.pdf Convex Geometry]. |

+ | |||

+ | Basically, the question asks whether all faces can be defined by intersection with a supporting hyperplane; that intersection is termed ''exposure.'' |

## Revision as of 20:40, 26 June 2008

The question remains open whether all faces of the cone of Euclidean distance matrices

**(**whose dimension is less than dimension of the cone**)**

are exposed like they are for the positive semidefinite cone.

For a better explanation, see section 6.5.3 in Cone of Distance Matrices.

Definition of *exposure* is in Convex Geometry.

Basically, the question asks whether all faces can be defined by intersection with a supporting hyperplane; that intersection is termed *exposure.*