# Euclidean distance cone faces

### From Wikimization

(Difference between revisions)

(RrDVOQPSJeliqIpkC) |
m (Reverted edits by 202.99.29.27 (Talk); changed back to last version by Dattorro) |
||

Line 1: | Line 1: | ||

- | + | The question remains open whether all faces of the cone of Euclidean distance matrices <math>\,\mathbb{EDM}^N\!</math> | |

+ | |||

+ | '''('''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 [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]. | ||

+ | |||

+ | 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 15:42, 11 November 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.*