Relaxations for Non-Separable Cardinality/Rank Penalties
(2021) In IEEE International Conference on Computer Vision Workshops p.162-171- Abstract
- Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can be described as separable, meaning that they apply a penalty to each element (or singular value) based on size, without considering the joint distribution. In this paper we present a class of non-separable penalties and give a recipe for computing strong relaxations suitable for optimization. In our analysis of this formulation we first give conditions that ensure that the global ly optimal solution of the relaxation is the same as that of the original (unrelaxed) objective. We then show how a stationary... (More)
- Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can be described as separable, meaning that they apply a penalty to each element (or singular value) based on size, without considering the joint distribution. In this paper we present a class of non-separable penalties and give a recipe for computing strong relaxations suitable for optimization. In our analysis of this formulation we first give conditions that ensure that the global ly optimal solution of the relaxation is the same as that of the original (unrelaxed) objective. We then show how a stationary point can be guaranteed to be unique under the restricted isometry property (RIP) assumption. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b6215171-7744-4eb7-97ea-2686c6843ad6
- author
- Olsson, Carl LU ; Gerosa, Daniele LU and Carlsson, Marcus LU
- organization
- publishing date
- 2021
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW)
- series title
- IEEE International Conference on Computer Vision Workshops
- pages
- 10 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85123050515
- ISSN
- 2473-9936
- 2473-9944
- ISBN
- 978-1-6654-0191-3
- 978-1-6654-0192-0
- DOI
- 10.1109/ICCVW54120.2021.00023
- language
- English
- LU publication?
- yes
- id
- b6215171-7744-4eb7-97ea-2686c6843ad6
- alternative location
- https://openaccess.thecvf.com/content/ICCV2021W/RSLCV/papers/Olsson_Relaxations_for_Non-Separable_CardinalityRank_Penalties_ICCVW_2021_paper.pdf
- date added to LUP
- 2021-11-17 13:05:37
- date last changed
- 2024-08-15 12:01:54
@inproceedings{b6215171-7744-4eb7-97ea-2686c6843ad6, abstract = {{Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can be described as separable, meaning that they apply a penalty to each element (or singular value) based on size, without considering the joint distribution. In this paper we present a class of non-separable penalties and give a recipe for computing strong relaxations suitable for optimization. In our analysis of this formulation we first give conditions that ensure that the global ly optimal solution of the relaxation is the same as that of the original (unrelaxed) objective. We then show how a stationary point can be guaranteed to be unique under the restricted isometry property (RIP) assumption.}}, author = {{Olsson, Carl and Gerosa, Daniele and Carlsson, Marcus}}, booktitle = {{2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW)}}, isbn = {{978-1-6654-0191-3}}, issn = {{2473-9936}}, language = {{eng}}, pages = {{162--171}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE International Conference on Computer Vision Workshops}}, title = {{Relaxations for Non-Separable Cardinality/Rank Penalties}}, url = {{http://dx.doi.org/10.1109/ICCVW54120.2021.00023}}, doi = {{10.1109/ICCVW54120.2021.00023}}, year = {{2021}}, }