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SUMMARY:Convex separation from convex optimization for large-scale problem
 s - Steve Brierley\, University of Cambridge
DTSTART:20161110T141500Z
DTEND:20161110T151500Z
UID:TALK68782@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:I'll present a new scheme to prove separation between a point 
 and an arbitrary convex set S via calls to an oracle able to perform linea
 r optimizations over S. Compared to other methods\, it has almost negligib
 le memory requirements and the number of calls to the optimization oracle 
 does not depend on the dimensionality of the underlying space. We study th
 e speed of convergence of the scheme under different promises on the shape
  of the set S and/or the location of the point\, validating the accuracy o
 f the theoretical bounds with numerical examples. \n\nI will then present 
 some applications of the scheme in quantum information theory. The algorit
 hm out-performs existing linear programming methods for certain large scal
 e problems\, allowing us to certify nonlocality in bipartite scenarios wit
 h upto 42 measurement settings. I'll show how to use the algorithm to uppe
 r bound the visibility of two-qubit Werner states\, hence improving known 
 lower bounds on Grothendieck's constant KG(3). Similarly\, we compute new 
 upper bounds on the visibility of GHZ states and on the steerability limit
  of Werner states for a fixed number of measurement settings.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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