Euclidean distance cone faces

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The question remains open whether all faces of the cone of Euclidean distance matrices <math>\,\mathbb{EDM}^N\!</math>
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'''('''whose dimension is less than dimension of the cone''')'''
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are exposed like they are for the positive semidefinite cone.
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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.''

Revision as of 15:42, 11 November 2009

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.

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