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SUMMARY:Gradient methods for huge-scale optimization problems - Yurii Nest
 erov\, Universite catholique de Louvain
DTSTART:20140527T163000Z
DTEND:20140527T173000Z
UID:TALK51772@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:We consider a new class of huge-scale problems\, the problems 
 with sparse gradients. The most important functions of this type are piece
 -wise linear. For optimization problems with uniform sparsity of correspon
 ding linear operators\, we suggest a very efficient implementation of the 
 iterations\, which total cost depends logarithmically in the dimension. Th
 is technique is based on a recursive update of the results of matrix/vecto
 r products and the values of symmetric functions. It works well\, for exam
 ple\, for matrices with few nonzero diagonals and for max-type functions. 
 We show that the updating technique can be efficiently coupled with the si
 mplest gradient methods. Similar results can be obtained for a new  non-sm
 ooth random variant of a coordinate descent scheme. We present also the pr
 omising results of preliminary computational experiments and discuss exten
 sions of this technique.
LOCATION:Cambridge University Engineering Department\, LR6
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