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SUMMARY:Low-Rank Inducing Norms with Optimality Interpretations - Christia
 n Grussler\, University of Lund
DTSTART:20170601T130000Z
DTEND:20170601T140000Z
UID:TALK72526@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:This talk is on optimization problems which are convex apart f
 rom a sparsity/rank constraint. These problems are often found in the cont
 ext of compressed sensing\, linear regression\, matrix completion\, low-ra
 nk approximation and many more. Since these problems are generally NP-hard
 \, today\, one of the most widely used methods for solving them is so-call
 ed nuclear norm regularization. Despite the nice probabilistic guarantees 
 of this method\, this approach often fails for problems with structural co
 nstraints.\n\nIn this talk\, we will present an alternative by introducing
  the family of so-called low-rank inducing norms as convexifiers. Each nor
 m is the convex envelope of a unitarily invariant norm plus a rank constra
 int. Therefore\, they have several interesting properties\, which will be 
 discussed throughout the talk. They:\n\ni. Give a simple deterministic tes
 t if the solution to the convexified problem is a solution to a specific n
 on-convex problem. \n\nii. Often finds solutions where the nuclear norm fa
 ils to give low-rank solutions.\n\niii. Allow us to analyze the convergenc
 e of non-convex proximal splitting algorithms with convex analysis tools. 
 \n\niv. Provide a more efficient regularization than the traditional scala
 r multiplication of the nuclear norm.  \n\nv. Leads to a different interpr
 etation of the nuclear norm than 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
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