TU Berlin

Fachgebiet Algorithmische AlgebraProf. Dr. Peter Bürgisser

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Prof. Dr. Peter Bürgisser

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Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 317 (3. OG)
Institut für Mathematik

Kontakt

Sekretariat
Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
peter.buergisser@offmath.tu-berlin.de

Telefon
+49 (0)30 314 - 75902
Faxgerät
+49 (0)30 314 - 25839

Sprechstunde
Während der Vorlesungszeit: Do, 15-16 Uhr.
Während der vorlesungsfreien Zeit: nach Vereinbarung.

Publikationen

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.
Link to publication Link to original publication Download Bibtex entry

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