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CATEGORIES:CUED Control Group Seminars
SUMMARY:Low-Rank Inducing Norms with Optimality Interpreta
tions - Christian Grussler\, University of Lund
DTSTART;TZID=Europe/London:20170601T140000
DTEND;TZID=Europe/London:20170601T150000
UID:TALK72526AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72526
DESCRIPTION:This talk is on optimization problems which are co
nvex apart from a sparsity/rank constraint. These
problems are often found in the context of compres
sed sensing\, linear regression\, matrix completio
n\, low-rank approximation and many more. Since th
ese problems are generally NP-hard\, today\, one o
f the most widely used methods for solving them is
so-called nuclear norm regularization. Despite th
e nice probabilistic guarantees of this method\, t
his approach often fails for problems with structu
ral constraints.\n\nIn this talk\, we will present
an alternative by introducing the family of so-ca
lled low-rank inducing norms as convexifiers. Each
norm is the convex envelope of a unitarily invari
ant norm plus a rank constraint. Therefore\, they
have several interesting properties\, which will b
e discussed throughout the talk. They:\n\ni. Give
a simple deterministic test if the solution to the
convexified problem is a solution to a specific n
on-convex problem. \n\nii. Often finds solutions w
here the nuclear norm fails to give low-rank solut
ions.\n\niii. Allow us to analyze the convergence
of non-convex proximal splitting algorithms with c
onvex analysis tools. \n\niv. Provide a more effic
ient regularization than the traditional scalar mu
ltiplication of the nuclear norm. \n\nv. Leads to
a different interpretation of the nuclear norm th
an the one that is traditionally presented.\n\nIn
particular\, all the results can be generalized to
so-called atomic norms.
LOCATION:Cambridge University Engineering Department\, LR12
CONTACT:Tim Hughes
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