A new class of sets regularity

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dc.contributor.author Nour, Chadi
dc.contributor.author Takche, Jean
dc.date.accessioned 2020-03-12T14:08:09Z
dc.date.available 2020-03-12T14:08:09Z
dc.date.copyright 2018 en_US
dc.date.issued 2020-03-12
dc.identifier.issn 0944-6532 en_US
dc.identifier.uri http://hdl.handle.net/10725/11865
dc.description.abstract Let A ⊂ R n be a closed set and let S ⊂ R n be a set containing A. In this paper we study a new regularity class for A, called S-convexity, introduced by C. Nour, H. Saoud and J. Takche [Regularization via sets satisfying the interior sphere condition, J. Convex Analysis 25(1) (2018)], where an inner approximation of a closed set by sets satisfying the interior sphere condition is given. We prove that this new class covers several known regularity properties including the proximal smoothness, the exterior sphere condition and the union of closed balls. As an application of such results, we provide a new sufficient condition for the equivalence between proximal smoothness and the exterior sphere condition studied previously by C. Nour, R. J. Stern and J. Takche [Proximal smoothness and the exterior sphere condition, J. Convex Analysis 16(2) (2009) 501–514]. en_US
dc.language.iso en en_US
dc.title A new class of sets regularity en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SAS en_US
dc.author.idnumber 200502681 en_US
dc.author.idnumber 198790400 en_US
dc.author.department Computer Science And Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal Journal of Convex Analysis en_US
dc.journal.volume 25 en_US
dc.journal.issue 4 en_US
dc.article.pages 1059-1074 en_US
dc.keywords S-convexity en_US
dc.keywords Proximal smoothness en_US
dc.keywords Exterior sphere condition en_US
dc.keywords Union of closed balls property en_US
dc.keywords Proximal analysis en_US
dc.keywords Nonsmooth analysis en_US
dc.identifier.ctation Nour, C. and Takche J. (2018). A new class of sets regularity. Journal of Convex Analysis 25 (4), 1059-1074. en_US
dc.author.email chadi.nour@lau.edu.lb en_US
dc.author.email jtakshi@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php en_US
dc.identifier.url https://www.heldermann.de/JCA/JCA25/JCA254/jca25068.htm en_US
dc.orcid.id https://orcid.org/0000-0003-4378-7459 en_US
dc.orcid.id https://orcid.org/0000-0003-3328-8330 en_US
dc.author.affiliation Lebanese American University en_US

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