BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:CCIMI Seminars
SUMMARY:Finding stationary points on the bounded-rank vari
ety: a geometric hurdle and a smooth workaround -
Nicolas Boumal (EPFL)
DTSTART;TZID=Europe/London:20210505T140000
DTEND;TZID=Europe/London:20210505T150000
UID:TALK156319AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/156319
DESCRIPTION:The set of matrices of a certain size and rank is
a smooth manifold. Unfortunately\, it is not close
d: this is uncomfortable for optimization. The clo
sure of that manifold\, namely\, the set of matric
es with bounded rank\, is an algebraic variety but
it is not smooth. That also is uncomfortable for
optimization. Case in point\, the norm of the (pro
jected) gradient of the cost function can go to ze
ro along a sequence even if the limit point of the
sequence is not stationary. This can trick algori
thms. I will characterize the geometry of this phe
nomenon. Then\, I will discuss how lifting the pro
blem to a smooth manifold makes it possible to con
verge to stationary points with certainty under mi
ld conditions.\n\nJoint work with Eitan Levin (Cal
Tech) and Joe Kileel (UT Austin).
LOCATION:Online (Join Zoom Meeting https://us02web.zoom.us/
j/81608191565?pwd=RDR2Uk1pU1Y3bHdZV3Q0SFlWdVYzdz09
)
CONTACT:Hamza Fawzi
END:VEVENT
END:VCALENDAR