# Euclidean distance cone faces

### From Wikimization

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Current revision (16:42, 11 November 2009) (edit) (undo)m (Protected "Euclidean distance cone faces" [edit=autoconfirmed:move=autoconfirmed]) |
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are exposed like they are for the positive semidefinite cone. | are exposed like they are for the positive semidefinite cone. | ||

- | 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]. |

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

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+ | Basically, the question asks whether all faces of <math>\,\mathbb{EDM}^N\!</math> can be defined by intersection with a supporting hyperplane; that intersection is termed ''exposure.'' |

## Current revision

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 of can be defined by intersection with a supporting hyperplane; that intersection is termed *exposure.*