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SUMMARY:A Riemannian approach to large scale constrained least squares wit
 h symmetries - Bamdev Mishra\, University of Liege/ University of Cambridg
 e
DTSTART:20140508T130000Z
DTEND:20140508T140000Z
UID:TALK52106@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:Least squares optimization on a manifold of equivalence relati
 ons\, i.e.\, in the presence of symmetries\, appears  in many fields. Two
  fundamental examples are the generalized eigenvalue problem\, a least-squ
 are problem with orthogonality constraints\, and the matrix completion pro
 blem\, a least-square problem with rank constraints. The large scale natu
 re of these problems requires us to exploit the problem structure as much 
 as possible. The presentation deals with these structures.\n\nRiemannian o
 ptimization has gained much popularity in the recent years because of the 
 particular nature of the orthogonality and rank constraints. Previous wor
 k on Riemannian optimization has mostly focused on the search space\, expl
 oiting the differential geometry of the constraint but disregarding the ro
 le of the cost function.\n\nWe show a basic connection between sequential
  quadratic programming and Riemannian gradient optimization and address th
 e general question of selecting a metric in Riemannian optimization in a w
 ay that not only exploits the constraints but also the cost function\, tha
 t is\, exploits the least squares problem structure. \n\nThe proposed met
 hod of selecting a Riemannian metric is shown to be particularly insightfu
 l and efficient in quadratic optimization with orthogonality and rank cons
 traints\, which covers most current applications of Riemannian optimizatio
 n in matrix manifolds. \n\nKeywords: Riemannian optimization Sequential q
 uadratic programming\, Metric\, Preconditioning\, Orthogonality\, Low-rank
LOCATION:Cambridge University Engineering Department\, LR6
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