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SUMMARY:Nonlinear Fenchel Conjugates
DTSTART:20241129T101500
DTEND:20241129T111500
DTSTAMP:20260411T071831Z
UID:59386fb224f0a6ce88fee1dba83135b70252d32b9498f54252c54c59
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ronny Bergmann (NTNU Norway)\nFenchel conjugates play an impor
 tant role in nonsmooth optimization.\nEspecially in large scale\, nonsmoot
 h problems\, like image processing\, splitting methods\nenable fast and ef
 ficient optimisation algorithms based on Fenchel duality.\nRecently\, a fe
 w different variants of Fenchel conjugates have been introduced on Manifol
 ds.\nThe main challenge is\, that the original Fenchel conjugate is define
 d as a supremum over\nlinear functions\, which do not exist on manifolds.\
 n\nIn this talk we present a generalisation\, the so-called nonlinear Fenc
 hel conjugates.\nWe discuss\, which properties can still be derived\, for 
 example how a biconjugate can be\nintroduced and how the relation between 
 convolution and the Fenchel conjugate\nare generalized to Lie groups.\nAs 
 an application we present the Primal-Dual-Hybrid-Gradient or Chambolle-Poc
 k algorithm\nand illustrate its performance in an image denoising task for
  manifold-valued images.
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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