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DTSTART:20251026T030000
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UID:calendar.137687.field_date.0@www.tse-fr.eu
DTSTAMP:20260510T205800Z
CREATED:20250711T141001Z
DESCRIPTION:Pierre Cyril Aubin (CERMICS-ENPC)\, “A flow for every c(x\,y) c
 ost: the hidden geometry of optimization algorithms”\, MAD-Stat. Seminar\,
  Toulouse: TSE\, September 25\, 2025\, 11:00–12:15\, room Auditorium 3.\n
 \nHow to go beyond the square distance d² in optimization algorithms and f
 lows in metric spaces? Replacing it with a general cost function c(x\,y) a
 nd using a majorize-minimize framework I will detail a generic class of al
 gorithms encompassing Newton/mirror/natural/Riemannian gradient descent/Si
 nkhorn/EM by reframing them as an alternating minimization\, each for a di
 fferent cost c(x\,y). Rooted in cross-differences\, the convergence theory
  to the infimum and to the continuous flow is investigated is based on a (
 discrete) evolution variational inequality (EVI) which enjoys similar prop
 erties to the EVI with d² regularizer. This provides a theoretical framewo
 rk for studying splitting schemes beyond the usual implicit Euler in gradi
 ent flows. This talk is based on the works https://arxiv.org/abs/2305.0491
 7 with Flavien Léger (INRIA Paris)\, and https://arxiv.org/abs/2505.00559 
 with Giacomo Sodini and Ulisse Stefanelli (Uni Vienna).
DTSTART;TZID=Europe/Paris:20250925T120000
DTEND;TZID=Europe/Paris:20250925T131500
LAST-MODIFIED:20251022T001001Z
LOCATION:Toulouse: TSE\, September 25\, 2025\, 11:00–12:15\, room Auditoriu
 m 3
SUMMARY:MAD-Stat. Seminar
URL;TYPE=URI:https://www.tse-fr.eu/seminars/2025-flow-every-cxy-cost-hidden
 -geometry-optimization-algorithms
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