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Local convergence of proximal splitting methods for rank constrained problems

Grussler, Christian LU and Giselsson, Pontus LU orcid (2018) 56th IEEE 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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
volume
2018-January
pages
7 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
56th IEEE Annual Conference on Decision and Control, CDC 2017
conference location
Melbourne, Australia
conference dates
2017-12-12 - 2017-12-15
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
2023-10-20 04:23:41
@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    = {{IEEE - 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}},
  doi          = {{10.1109/CDC.2017.8263743}},
  volume       = {{2018-January}},
  year         = {{2018}},
}