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SUMMARY:Canonical barriers on convex cones
DTSTART;VALUE=DATE-TIME:20161207T134000Z
DTEND;VALUE=DATE-TIME:20161207T143000Z
DTSTAMP;VALUE=DATE-TIME:20210617T194552Z
UID:indico-event-1749@indico.math.cnrs.fr
DESCRIPTION:The Calabi theorem states that for every regular convex cone K
in R^n\, the Monge-Ampère equation log det F” = 2F/n has a unique conv
ex solution on the interior of K which tends to +infty on the boundary of
K. It turns out that this solution is self-concordant and logarithmically
homogeneous\, and thus is a barrier which can be used for conic optimizati
on. We consider different aspects of this barrier:\n\n\n affine spheres
as level surfaces\n metrization of the interior of K by the Hessian me
tric F”\n primal-dual symmetry\n interpretation as a minimal Lagra
ngian submanifold in a certain para-Kähler space form\n complex-analyt
ic structure on 3-dimensional cones.\n\n\nhttps://indico.math.cnrs.fr/even
t/1749/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/1749/
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