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Article: Restarting the accelerated coordinate descent method with a rough strong convexity estimate
Title | Restarting the accelerated coordinate descent method with a rough strong convexity estimate |
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Authors | |
Keywords | Accelerated coordinate descent Restarting strategies Unknown strong convexity Local quadratic error bound |
Issue Date | 2020 |
Publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0926-6003 |
Citation | Computational Optimization and Applications, 2020, v. 75, p. 63-91 How to Cite? |
Abstract | We propose new restarting strategies for the accelerated coordinate descent method. Our main contribution is to show that for a well chosen sequence of restarting times, the restarted method has a nearly geometric rate of convergence. A major feature of the method is that it can take profit of the local quadratic error bound of the objective function without knowing the actual value of the error bound. We also show that under the more restrictive assumption that the objective function is strongly convex, any fixed restart period leads to a geometric rate of convergence. Finally, we illustrate the properties of the algorithm on a regularized logistic regression problem and on a Lasso problem. |
Persistent Identifier | http://hdl.handle.net/10722/290916 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 1.322 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Fercoq, O | - |
dc.contributor.author | Qu, Z | - |
dc.date.accessioned | 2020-11-02T05:48:55Z | - |
dc.date.available | 2020-11-02T05:48:55Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Computational Optimization and Applications, 2020, v. 75, p. 63-91 | - |
dc.identifier.issn | 0926-6003 | - |
dc.identifier.uri | http://hdl.handle.net/10722/290916 | - |
dc.description.abstract | We propose new restarting strategies for the accelerated coordinate descent method. Our main contribution is to show that for a well chosen sequence of restarting times, the restarted method has a nearly geometric rate of convergence. A major feature of the method is that it can take profit of the local quadratic error bound of the objective function without knowing the actual value of the error bound. We also show that under the more restrictive assumption that the objective function is strongly convex, any fixed restart period leads to a geometric rate of convergence. Finally, we illustrate the properties of the algorithm on a regularized logistic regression problem and on a Lasso problem. | - |
dc.language | eng | - |
dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0926-6003 | - |
dc.relation.ispartof | Computational Optimization and Applications | - |
dc.rights | This is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI] | - |
dc.subject | Accelerated coordinate descent | - |
dc.subject | Restarting strategies | - |
dc.subject | Unknown strong convexity | - |
dc.subject | Local quadratic error bound | - |
dc.title | Restarting the accelerated coordinate descent method with a rough strong convexity estimate | - |
dc.type | Article | - |
dc.identifier.email | Qu, Z: zhengqu@hku.hk | - |
dc.identifier.authority | Qu, Z=rp02096 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s10589-019-00137-2 | - |
dc.identifier.scopus | eid_2-s2.0-85074521068 | - |
dc.identifier.hkuros | 317753 | - |
dc.identifier.volume | 75 | - |
dc.identifier.spage | 63 | - |
dc.identifier.epage | 91 | - |
dc.identifier.isi | WOS:000511695500003 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0926-6003 | - |