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Metric and Geometric Relaxations of Self-Contracted Curves

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dc.contributor.authorDaniilidis, Aris
dc.contributor.authorDeville, Robert
dc.contributor.orcidhttps://orcid.org/0000-0003-4837-694X
dc.date.accessioned2024-12-03T13:36:02Z
dc.date.available2024-12-03T13:36:02Z
dc.date.issued2018-10-13
dc.descriptionThe registered version of this article, first published in Journal of Optimization Theory and Applications, is available online at the publisher's website: Springer Nature, https://doi.org/10.1007/s10957-018-1408-0
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Journal of Optimization Theory and Applications, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s10957-018-1408-0
dc.description.abstractThe metric notion of a self-contracted curve (respectively, self-expanded curve, if we reverse the orientation) is hereby extended in a natural way. Two new classes of curves arise from this extension, both depending on a parameter, a specific value of which corresponds to the class of self-expanded curves. The first class is obtained via a straightforward metric generalization of the metric inequality that defines self-expandedness, while the second one is based on the (weaker) geometric notion of the so-called cone property (eel-curve). In this work, we show that these two classes are different; in particular, curves from these two classes may have different asymptotic behavior. We also study rectifiability of these curves in the Euclidean space, with emphasis in the planar case.en
dc.description.versionversión final
dc.identifier.citationDaniilidis, A., Deville, R. & Durand-Cartagena, E. Metric and Geometric Relaxations of Self-Contracted Curves. J Optim Theory Appl 182, 81–109 (2019). https://doi.org/10.1007/s10957-018-1408-0
dc.identifier.doihttps://doi.org/10.1007/s10957-018-1408-0
dc.identifier.issn1573-2878
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24678
dc.journal.titleJournal of Optimization Theory and Applications
dc.journal.volume182
dc.language.isoen
dc.page.final109
dc.page.initial81
dc.publisherSpringer Nature
dc.relation.centerFacultades y escuelas::E.T.S. de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsself-contracted curveen
dc.subject.keywordsself-expanded curveen
dc.subject.keywordsrectifiabilityen
dc.subject.keywordslengthen
dc.subject.keywordsλ-curveen
dc.subject.keywordsλ-cone propertyen
dc.titleMetric and Geometric Relaxations of Self-Contracted Curvesen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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