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SUMMARY:Numerical shape optimization among convex sets
DTSTART;VALUE=DATE-TIME:20221017T083000Z
DTEND;VALUE=DATE-TIME:20221017T093000Z
DTSTAMP;VALUE=DATE-TIME:20221128T111000Z
UID:indico-event-8255@indico.math.cnrs.fr
CONTACT:laborde@math.univ-paris-diderot.fr
DESCRIPTION:Speakers: Beniamin Bogosel\n\nOptimization of shape functional
s under convexity\, diameter or constant width constraints is challenging
from a numerical point of view. The support and gauge functions allow a fu
nctional characterization of these constraints. Functions describing conve
x sets are discretized using truncated spectral decompositions or values o
n a uniform grid. I will present the resulting numerical frameworks\, toge
ther with various applications from convex geometry and spectral optimizat
ion. In the second part of the talk\, I will discuss a different point of
view on constrained optimization problems. The Blaschke-Santalo diagrams
can completely characterize all possible inequalities between various qu
antites\, under eventual constraints. The complete theoretical characteriz
ation of such diagrams is often difficult to obtain\, motivating the inter
est in algorithms allowing their numerical approximations. Recent developm
ents related to this topic\, with applications in algebra and convex geome
try\, will be presented. In this process\, yet another discretization proc
ess for convex shapes is proposed.\n\nhttps://indico.math.cnrs.fr/event/82
55/
LOCATION:Université Paris-Cité (campus Grands Moulins)
URL:https://indico.math.cnrs.fr/event/8255/
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