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SUMMARY:Convex Analysis in Hadamard Spaces - Gabriele Steidl (University o
 f Kaiserslautern)
DTSTART:20170906T151000Z
DTEND:20170906T160000Z
UID:TALK78121@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>joint work with M. Bacak\, R. Bergmann\, M. Montag and J
 . Persch<br> <br></span><span>The aim of the talk is two-fold:<br><br> 1. 
 A well known result of H. Attouch states that the Mosco convergence&nbsp\;
 of a sequence of proper convex lower semicontinuous functions&nbsp\;define
 d on a Hilbert space is equivalent to the pointwise convergence&nbsp\;of t
 he associated Moreau envelopes.&nbsp\;In the present paper we generalize t
 his result to Hadamard spaces.&nbsp\;More precisely\, while it has already
  been known that the Mosco convergence of a sequence of convex lower semic
 ontinuous functions on a Hadamard space implies the pointwise convergence 
 of the corresponding Moreau envelopes\, the converse implication was an op
 en question. We now fill this gap.&nbsp\; Our result has several consequen
 ces. It implies\, for instance\, the equivalence of the Mosco and Frolik-W
 ijsman convergences of convex sets.&nbsp\;As another application\, we show
  that there exists a~complete metric on the cone of proper convex lower se
 micontinuous functions on a separable Hadamard space such that a~sequence 
 of functions converges in this metric if and only if it converges in the s
 ense of Mosco.<br><br> 2. We extend the parallel Douglas-Rachford algorith
 m&nbsp\; to the manifold-valued setting.<br> </span>
LOCATION:Seminar Room 1\, Newton Institute
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