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Convex envelopes for fixed rank approximation

Andersson, Fredrik LU ; Carlsson, Marcus LU and Olsson, Carl LU (2017) In Optimization Letters 11(8). p.1783-1795
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.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Approximation, Convex envelope, Proximity operator, Rank constraint
in
Optimization Letters
volume
11
issue
8
pages
1783 - 1795
publisher
Springer
external identifiers
  • wos:000415197500021
  • scopus:85018762595
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
2024-06-23 17:55:12
@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}},
  keywords     = {{Approximation; Convex envelope; Proximity operator; Rank constraint}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{1783--1795}},
  publisher    = {{Springer}},
  series       = {{Optimization Letters}},
  title        = {{Convex envelopes for fixed rank approximation}},
  url          = {{http://dx.doi.org/10.1007/s11590-017-1146-5}},
  doi          = {{10.1007/s11590-017-1146-5}},
  volume       = {{11}},
  year         = {{2017}},
}