Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/7015
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | - |
dc.creator | Bian, W | - |
dc.creator | Chen, X | - |
dc.date.accessioned | 2014-12-11T08:26:18Z | - |
dc.date.available | 2014-12-11T08:26:18Z | - |
dc.identifier.issn | 1052-6234 | - |
dc.identifier.uri | http://hdl.handle.net/10397/7015 | - |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.rights | © 2013 Society for Industrial and Applied Mathematics | en_US |
dc.subject | Nonsmooth nonconvex optimization | en_US |
dc.subject | Smoothing approximation | en_US |
dc.subject | Quadratic regularization | en_US |
dc.subject | Convergence | en_US |
dc.subject | Worst-case complexity | en_US |
dc.subject | Stationary point | en_US |
dc.title | Worst-case complexity of smoothing quadratic regularization methods for non-lipschitzian optimization | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 1718 | - |
dc.identifier.epage | 1741 | - |
dc.identifier.volume | 23 | - |
dc.identifier.issue | 3 | - |
dc.identifier.doi | 10.1137/120864908 | - |
dcterms.abstract | In this paper, we propose a smoothing quadratic regularization (SQR) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitzian minimization problems, which has wide applications in statistics and sparse reconstruction. The proposed SQR algorithm is a first order method. At each iteration, the SQR algorithm solves a strongly convex quadratic minimization problem with a diagonal Hessian matrix, which has a simple closed-form solution that is inexpensive to calculate. We show that the worst-case complexity of reaching an ϵ scaled stationary point is $O(ϵ⁻²). Moreover, if the objective function is locally Lipschitz continuous, the SQR algorithm with a slightly modified updating scheme for the smoothing parameter and iterate can obtain an ϵ Clarke stationary point in at most $O(ϵ⁻³) iterations. | - |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | SIAM Journal on optimization, 2013, v. 23, no. 3, p. 1718–1741 | - |
dcterms.isPartOf | SIAM Journal on optimization | - |
dcterms.issued | 2013 | - |
dc.identifier.isi | WOS:000325094000015 | - |
dc.identifier.scopus | 2-s2.0-84886302151 | - |
dc.identifier.eissn | 1095-7189 | - |
dc.identifier.rosgroupid | r72398 | - |
dc.description.ros | 2013-2014 > Academic research: refereed > Publication in refereed journal | - |
dc.description.oa | Version of Record | en_US |
dc.identifier.FolderNumber | OA_IR/PIRA | en_US |
dc.description.pubStatus | Published | en_US |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Bian_Worst-case_Complexity_quadratic.pdf | 579.7 kB | Adobe PDF | View/Open |
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