# Euclidean distance cone faces

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m (Euclidean distance cone moved to Euclidean distance cone faces: This is an open question.) |
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The question remains open whether all faces of the cone of Euclidean distance matrices <math>\,\mathbb{EDM}^N\!</math> | The question remains open whether all faces of the cone of Euclidean distance matrices <math>\,\mathbb{EDM}^N\!</math> | ||

- | '''('''whose dimension is less than | + | |

+ | '''('''whose dimension is less than dimension of the cone''')''' | ||

+ | |||

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]. | ||

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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.*