# Euclidean distance cone faces

(Difference between revisions)
 Revision as of 10:51, 11 November 2009 (edit) (RrDVOQPSJeliqIpkC)← Previous diff Current revision (15:42, 11 November 2009) (edit) (undo)m (Protected "Euclidean distance cone faces" [edit=autoconfirmed:move=autoconfirmed]) (2 intermediate revisions not shown.) Line 1: Line 1: - Be9IGK kcgvsxspxfiz, [url=http://qpnvmnnsugnc.com/]qpnvmnnsugnc[/url], [link=http://ejdrozqrexlq.com/]ejdrozqrexlq[/link], http://zjcypltghuqw.com/ + The question remains open whether all faces of the cone of Euclidean distance matrices \,\mathbb{EDM}^N\! + + '''('''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 [itex]\,\mathbb{EDM}^N\! 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 $LaTeX: \,\mathbb{EDM}^N\!$

(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 $LaTeX: \,\mathbb{EDM}^N\!$ can be defined by intersection with a supporting hyperplane; that intersection is termed exposure.