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Intrinsic volumes of symmetric cones and applications in convex programming
Zitatschlüssel AB-Intrinsic-Volumes-Of-Symmetric-Cones-And-Applications-In-Convex-Programming
Autor Dennis Amelunxen and Peter Bürgisser
Seiten 105-130
Jahr 2015
Journal Mathematical Programming
Jahrgang 149
Nummer 1-2
Notiz This is a substantially revised and shortened version of the paper "Intrinsic volumes of symmetric cones" [arXiv 1205.1863]
Zusammenfassung We express the probability distribution of the solution of a random (standard Gaussian) instance of a convex cone program in terms of the intrinsic volumes and curvature measures of the reference cone. We then compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions in terms of integrals related to Mehta's integral. In particular, we obtain a closed formula for the probability that the solution of a random (standard Gaussian) semidefinite program has a certain rank.
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