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SUMMARY:Finding stationary points on the bounded-rank variety: a geometric
  hurdle and a smooth workaround - Nicolas Boumal (EPFL)
DTSTART:20210505T130000Z
DTEND:20210505T140000Z
UID:TALK156319@talks.cam.ac.uk
CONTACT:Hamza Fawzi
DESCRIPTION:The set of matrices of a certain size and rank is a smooth man
 ifold. Unfortunately\, it is not closed: this is uncomfortable for optimiz
 ation. The closure of that manifold\, namely\, the set of matrices with bo
 unded rank\, is an algebraic variety but it is not smooth. That also is un
 comfortable for optimization. Case in point\, the norm of the (projected) 
 gradient of the cost function can go to zero along a sequence even if the 
 limit point of the sequence is not stationary. This can trick algorithms. 
 I will characterize the geometry of this phenomenon. Then\, I will discuss
  how lifting the problem to a smooth manifold makes it possible to converg
 e to stationary points with certainty under mild conditions.\n\nJoint work
  with Eitan Levin (CalTech) and Joe Kileel (UT Austin).
LOCATION:Online (Join Zoom Meeting https://us02web.zoom.us/j/81608191565?p
 wd=RDR2Uk1pU1Y3bHdZV3Q0SFlWdVYzdz09)
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