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Local convergence of proximal splitting methods for rank constrained problems

Grussler, Christian LU and Giselsson, Pontus LU (2018) 56th IEEE Annual Conference on Decision and Control, CDC 2017 In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 2018-January. p.702-708
Abstract

We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hence implying local convergence. The conditions imply that the non-convex algorithms locally converge to a solution whenever a convex relaxation involving the convex envelope can be expected to solve the non-convex problem.

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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
volume
2018-January
pages
7 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
56th IEEE Annual Conference on Decision and Control, CDC 2017
external identifiers
  • scopus:85046116353
ISBN
9781509028733
DOI
10.1109/CDC.2017.8263743
language
English
LU publication?
yes
id
4f4acfd8-f8d8-4647-bb6b-f8ac2d5311f6
date added to LUP
2018-05-15 13:37:46
date last changed
2018-05-15 13:37:46
@inproceedings{4f4acfd8-f8d8-4647-bb6b-f8ac2d5311f6,
  abstract     = {<p>We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hence implying local convergence. The conditions imply that the non-convex algorithms locally converge to a solution whenever a convex relaxation involving the convex envelope can be expected to solve the non-convex problem.</p>},
  author       = {Grussler, Christian and Giselsson, Pontus},
  booktitle    = {2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017},
  isbn         = {9781509028733},
  language     = {eng},
  month        = {01},
  pages        = {702--708},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {Local convergence of proximal splitting methods for rank constrained problems},
  url          = {http://dx.doi.org/10.1109/CDC.2017.8263743},
  volume       = {2018-January},
  year         = {2018},
}