# Euclidean distance cone faces

### From Wikimization

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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.'' | + | 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.'' |

## Revision as of 21:47, 11 January 2009

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.*