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SUMMARY:Inertial primal dual splitting methods - Dirk Lorenz (Technische U
 niversität Braunschweig)
DTSTART:20131010T140000Z
DTEND:20131010T150000Z
UID:TALK44385@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:Many problems in mathematical imaging can be phrased as convex
  minimization problems or convex-concave saddle point problems. In both ca
 ses\, the respective optimality system is an inclusion with a (maximally) 
 monotone operator. To solve these inclusions\, several splitting methods h
 ave been proposed which rely on the idea that the monotone operator can be
  split up into simpler parts for which\, e.g. the resolvent can be applied
  easily.\n\nIn this talk we present a fairly general splitting method whic
 h works for inclusions in which the operator can be split such that one op
 erator is co-coercive and for the other a certain preconditioned resolvent
  is easily applicable. We arrive at an inertial forward backward splitting
  method for which we prove weak convergence under fairly general assumptio
 ns. It is show that the methods covers several existing methods such as Po
 lyak's heavy ball method\, Nesterov's accelerated gradient descent\, the f
 orward-backward splitting method and Beck and Teboulle's FISTA. We illustr
 ate the applicability and performance on numerous problems such as the Rud
 in-Osher-Fatemi denoising and deconvolution or the Osher-Sole-Vese denoisi
 ng.\n\nThis is joint work with Thomas Pock (TU Graz).\n
LOCATION:MR 14\, CMS
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