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dc.contributor.authorCurtis, F. E.
hal.structure.identifier
dc.contributor.authorRobinson, D. P.
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorRoyer, Clément
HAL ID: 734626
ORCID: 0000-0003-2452-2172
hal.structure.identifier
dc.contributor.authorWright, S. J.
dc.date.accessioned2021-04-12T13:17:02Z
dc.date.available2021-04-12T13:17:02Z
dc.date.issued2019
dc.identifier.issn1052-6234
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21660
dc.language.isoenen
dc.subjectsmooth nonconvex optimizationen
dc.subjecttrust-region methodsen
dc.subjectNewton's methoden
dc.subjectconjugate gradient methoden
dc.subjectLanczos methoden
dc.subjectworst-case complexityen
dc.subjectnegative curvatureen
dc.subject.ddc518en
dc.titleTrust-Region Newton-CG with Strong Second-Order Complexity Guarantees for Nonconvex Optimizationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWorst-case complexity guarantees for nonconvex optimization algorithms have been a topic of growing interest. Multiple frameworks that achieve the best known complexity bounds among a broad class of first- and second-order strategies have been proposed. These methods have often been designed primarily with complexity guarantees in mind and, as a result, represent a departure from the algorithms that have proved to be the most effective in practice. In this paper, we consider trust-region Newton methods, one of the most popular classes of algorithms for solving nonconvex optimization problems. By introducing slight modifications to the original scheme, we obtain two methods---one based on exact subproblem solves and one exploiting inexact subproblem solves as in the popular “trust-region Newton-conjugate gradient” (trust-region Newton-CG) method---with iteration and operation complexity bounds that match the best known bounds for the aforementioned class of first- and second-order methods. The resulting trust-region Newton-CG method also retains the attractive practical behavior of classical trust-region Newton-CG, which we demonstrate with numerical comparisons on a standard benchmark test set.en
dc.relation.isversionofjnlnameSIAM Journal on Optimization
dc.relation.isversionofjnlvol31en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2021-02
dc.relation.isversionofjnlpages518-544en
dc.relation.isversionofdoi10.1137/19M130563Xen
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematicsen
dc.subject.ddclabelModèles mathématiques. Algorithmesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-04-12T13:12:59Z
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