TU Berlin

Fachgebiet Algorithmische AlgebraDr. Dennis Amelunxen

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Ehemalige Mitarbeiter

Dr. Dennis Amelunxen


City University of Hong Kong
Department of Mathematics
G6613 (Green Zone), 6/F Academic 1
Tat Chee Avenue, Kowloon Tong, Hong Kong
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Publikationen in der Arbeitsgruppe

Intrinsic volumes of symmetric cones and applications in convex programming
Citation key AB-Intrinsic-Volumes-Of-Symmetric-Cones-And-Applications-In-Convex-Programming
Author Dennis Amelunxen and Peter Bürgisser
Pages 105-130
Year 2015
Journal Mathematical Programming
Volume 149
Number 1-2
Note This is a substantially revised and shortened version of the paper "Intrinsic volumes of symmetric cones" [arXiv 1205.1863]
Abstract 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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