Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/76268
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Liu, TX | en_US |
dc.creator | Pong, TK | en_US |
dc.date.accessioned | 2018-05-10T02:55:40Z | - |
dc.date.available | 2018-05-10T02:55:40Z | - |
dc.identifier.issn | 0926-6003 | en_US |
dc.identifier.uri | http://hdl.handle.net/10397/76268 | - |
dc.language.iso | en | en_US |
dc.publisher | Springer | en_US |
dc.rights | © Springer Science+Business Media New York 2017 | en_US |
dc.rights | This is a post-peer-review, pre-copyedit version of an article published in Computational Optimization and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10589-017-9900-2 | en_US |
dc.subject | Forward-backward envelope | en_US |
dc.subject | Kurdyka-Lojasiewicz property | en_US |
dc.subject | Difference-of-convex programming | en_US |
dc.title | Further properties of the forward-backward envelope with applications to difference-of-convex programming | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 489 | en_US |
dc.identifier.epage | 520 | en_US |
dc.identifier.volume | 67 | en_US |
dc.identifier.issue | 3 | en_US |
dc.identifier.doi | 10.1007/s10589-017-9900-2 | en_US |
dcterms.abstract | In this paper, we further study the forward-backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE Conference on Decision and Control, pp 2358-2363, 2013) and Stella et al. (Comput Optim Appl, doi:10.1007/s10589-017-9912-y, 2017) for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forward-backward envelope to be a level-bounded and Kurdyka-Aojasiewicz function with an exponent of ; these results are important for the efficient minimization of the forward-backward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some difference-of-convex regularized least squares problems by minimizing a suitably constructed forward-backward envelope. Our preliminary numerical results on randomly generated instances of large-scale regularized least squares problems (Yin et al. in SIAM J Sci Comput 37:A536-A563, 2015) illustrate that an implementation of this approach with a limited-memory BFGS scheme usually outperforms standard first-order methods such as the nonmonotone proximal gradient method in Wright et al. (IEEE Trans Signal Process 57:2479-2493, 2009). | en_US |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | Computational optimization and applications, July 2017, v. 67, no. 3, p. 489-520 | en_US |
dcterms.isPartOf | Computational optimization and applications | en_US |
dcterms.issued | 2017-07 | - |
dc.identifier.isi | WOS:000401999900002 | - |
dc.identifier.scopus | 2-s2.0-85012923479 | - |
dc.identifier.eissn | 1573-2894 | en_US |
dc.identifier.rosgroupid | 2017000099 | - |
dc.description.ros | 2017-2018 > Academic research: refereed > Publication in refereed journal | en_US |
dc.description.validate | 201805 bcrc | en_US |
dc.description.oa | Accepted Manuscript | en_US |
dc.identifier.FolderNumber | a0585-n01 | - |
dc.identifier.SubFormID | 280 | - |
dc.description.fundingSource | RGC | en_US |
dc.description.fundingText | 25300815 | en_US |
dc.description.pubStatus | Published | en_US |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
a0585-n01_FBE_nonconvex_re3.pdf | Pre-Published version | 1.14 MB | Adobe PDF | View/Open |
Page views
76
Last Week
0
0
Last month
Citations as of Oct 1, 2023
Downloads
66
Citations as of Oct 1, 2023
SCOPUSTM
Citations
33
Last Week
0
0
Last month
Citations as of Sep 28, 2023
WEB OF SCIENCETM
Citations
32
Last Week
0
0
Last month
Citations as of Sep 28, 2023

Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.