Euclidean distance cone faces

From Wikimization

Revision as of 22:47, 11 January 2009 by Dattorro (Talk | contribs)
Jump to: navigation, search

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.

Personal tools