Ehemalige Mitarbeiter

Dr. Dennis Amelunxen

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

Persönliche Homepage
sites.google.com/site/dennisamelunxen/home

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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