Optimality interpretations for atomic norms
Grussler, Christian LU and Giselsson, Pontus LU
(2019)
18th European Control Conference, ECC 2019
p.1473-1477
- Abstract
Atomic norms occur frequently in data science and engineering problems such as matrix completion, sparse linear regression, system identification and many more. These norms are often used to convexify non-convex optimization problems, which are convex apart from the solution lying in a non-convex set of so-called atoms. For the convex part being a linear constraint, the ability of several atomic norms to solve the original non-convex problem has been analyzed by means of tangent cones. This paper presents an alternative route for this analysis by showing that atomic norm convexifcations always provide an optimal convex relaxation for some related non-convex problems. As a result, we obtain the following benefits: (i) treatment of... (More)
Atomic norms occur frequently in data science and engineering problems such as matrix completion, sparse linear regression, system identification and many more. These norms are often used to convexify non-convex optimization problems, which are convex apart from the solution lying in a non-convex set of so-called atoms. For the convex part being a linear constraint, the ability of several atomic norms to solve the original non-convex problem has been analyzed by means of tangent cones. This paper presents an alternative route for this analysis by showing that atomic norm convexifcations always provide an optimal convex relaxation for some related non-convex problems. As a result, we obtain the following benefits: (i) treatment of arbitrary convex constraints, (ii) potentially obtaining solutions to the non-convex problem with a posteriori success certificates, (iii) utilization of additional prior knowledge through the design or learning of the non-convex problem.
(Less)
- author
- Grussler, Christian
LU
and Giselsson, Pontus
LU
- organization
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2019 18th European Control Conference, ECC 2019
- article number
- 8795721
- pages
- 5 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 18th European Control Conference, ECC 2019
- conference location
- Naples, Italy
- conference dates
- 2019-06-25 - 2019-06-28
- external identifiers
-
- scopus:85071594501
- ISBN
- 9783907144008
- DOI
- 10.23919/ECC.2019.8795721
- language
- English
- LU publication?
- yes
- id
- 43c9b01a-7bbd-4611-bf26-e2c5d97f3277
- date added to LUP
- 2019-09-20 08:19:36
- date last changed
- 2023-10-21 20:43:12
@inproceedings{43c9b01a-7bbd-4611-bf26-e2c5d97f3277,
abstract = {{<p>Atomic norms occur frequently in data science and engineering problems such as matrix completion, sparse linear regression, system identification and many more. These norms are often used to convexify non-convex optimization problems, which are convex apart from the solution lying in a non-convex set of so-called atoms. For the convex part being a linear constraint, the ability of several atomic norms to solve the original non-convex problem has been analyzed by means of tangent cones. This paper presents an alternative route for this analysis by showing that atomic norm convexifcations always provide an optimal convex relaxation for some related non-convex problems. As a result, we obtain the following benefits: (i) treatment of arbitrary convex constraints, (ii) potentially obtaining solutions to the non-convex problem with a posteriori success certificates, (iii) utilization of additional prior knowledge through the design or learning of the non-convex problem.</p>}},
author = {{Grussler, Christian and Giselsson, Pontus}},
booktitle = {{2019 18th European Control Conference, ECC 2019}},
isbn = {{9783907144008}},
language = {{eng}},
pages = {{1473--1477}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Optimality interpretations for atomic norms}},
url = {{http://dx.doi.org/10.23919/ECC.2019.8795721}},
doi = {{10.23919/ECC.2019.8795721}},
year = {{2019}},
}