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Convex envelopes for fixed rank approximation

Andersson, Fredrik LU ; Carlsson, Marcus LU and Olsson, Carl LU (2017) In Optimization Letters
Abstract

A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added to the finite rank approximation problem. Expression for the dependence of the convex envelope on the singular values of the given matrix is derived and global minimization properties are derived. The corresponding proximity operator is also studied.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Approximation, Convex envelope, Proximity operator, Rank constraint
in
Optimization Letters
pages
13 pages
publisher
Springer Verlag
external identifiers
  • scopus:85018762595
  • wos:000415197500021
ISSN
1862-4472
DOI
10.1007/s11590-017-1146-5
language
English
LU publication?
yes
id
63bd6d24-aaa5-4f44-99d1-5cf6686b8950
date added to LUP
2017-05-24 08:07:12
date last changed
2018-05-13 04:31:48
@article{63bd6d24-aaa5-4f44-99d1-5cf6686b8950,
  abstract     = {<p>A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added to the finite rank approximation problem. Expression for the dependence of the convex envelope on the singular values of the given matrix is derived and global minimization properties are derived. The corresponding proximity operator is also studied.</p>},
  author       = {Andersson, Fredrik and Carlsson, Marcus and Olsson, Carl},
  issn         = {1862-4472},
  keyword      = {Approximation,Convex envelope,Proximity operator,Rank constraint},
  language     = {eng},
  month        = {05},
  pages        = {13},
  publisher    = {Springer Verlag},
  series       = {Optimization Letters},
  title        = {Convex envelopes for fixed rank approximation},
  url          = {http://dx.doi.org/10.1007/s11590-017-1146-5},
  year         = {2017},
}