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SUMMARY:Analysis of the Adaptive Iterative Bregman Algorithm - Andreas Lan
 ger (RICAM)
DTSTART:20110128T160000Z
DTEND:20110128T170000Z
UID:TALK29583@talks.cam.ac.uk
CONTACT:Dan Brinkman
DESCRIPTION:In this talk we introduce and analyze the Adaptive Iterative B
 regman algorithm\, which can be viewed as a variation of other known Augme
 nted Lagrangian Methods for the solution of constrained optimization probl
 ems of the type\n\nmin J(v) subject to Av = f\, v∈H\n\nwhere J is a conv
 ex\, proper\, and lower semicontinuous functional on a Hilbert space H and
  Av = f is a linear constraint. The algorithm alternates a proximity map i
 teration\, based on forward-backward splitting\, and the iterative update 
 of a suitable Lagrange multiplier to\nenforce the linear constraint. We ca
 n show that\, at the cost of performing a small and adaptive number of inn
 er proximity map iterations\, we can gain extra properties for the propose
 d algorithm\, very desirable for concrete applications: in particular the 
 execution of the iterations is made simple by forward-backward splitting\,
  the discrepancy functional v → Av − f is monotone when evaluated on t
 he iterations\, and eventually we have guaranteed convergence to a solutio
 n of the given optimization problem.\n
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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