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CATEGORIES:Applied and Computational Analysis Graduate Semina
r
SUMMARY:Analysis of the Adaptive Iterative Bregman Algorit
hm - Andreas Langer (RICAM)
DTSTART;TZID=Europe/London:20110128T160000
DTEND;TZID=Europe/London:20110128T170000
UID:TALK29583AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29583
DESCRIPTION:In this talk we introduce and analyze the Adaptive
Iterative Bregman algorithm\, which can be viewed
as a variation of other known Augmented Lagrangia
n Methods for the solution of constrained optimiza
tion problems of the type\n\nmin J(v) subject to A
v = f\, vāH\n\nwhere J is a convex\, proper\, and
lower semicontinuous functional on a Hilbert space
H and Av = f is a linear constraint. The algorith
m alternates a proximity map iteration\, based on
forward-backward splitting\, and the iterative upd
ate of a suitable Lagrange multiplier to\nenforce
the linear constraint. We can show that\, at the c
ost of performing a small and adaptive number of i
nner proximity map iterations\, we can gain extra
properties for the proposed algorithm\, very desir
able for concrete applications: in particular the
execution of the iterations is made simple by forw
ard-backward splitting\, the discrepancy functiona
l v ā Av ā f is monotone when evaluated on the ite
rations\, and eventually we have guaranteed conver
gence to a solution of the given optimization prob
lem.\n
LOCATION:MR14\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:Dan Brinkman
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