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dc.contributor.authorChavent, Guy
dc.date.accessioned2014-10-30T14:01:21Z
dc.date.available2014-10-30T14:01:21Z
dc.date.issued1991
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14104
dc.language.isoenen
dc.subjectprojection theoryen
dc.subjectapproximation theoryen
dc.subjectnonlinear least squaresen
dc.subjectinverse problemsen
dc.subject.ddc519en
dc.titleNew Size x Curvature Conditions for Strict Quasiconvexity of Setsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenGiven a closed, not necessarily convex set D of a Hilbert space, the problem of the existence of a neighborhood $\mathcal{V}$ on which the projection on D is uniquely defined and Lipschitz continuous is considered, and such that the corresponding minimization problem has no local minima. After having equipped the set D with a family $\mathcal{P}$ of paths playing for D the role the segments play for a convex set, the notion of strict quasiconvexity of $(D,\mathcal{P})$ is defined, which will ensure the existence of such a neighborhood $\mathcal{V}$. Two constructive sufficient conditions for the strict-quasiconvexity of D are given, the $R_G $-size $ \times $ curvature condition and the $\Theta $-size $ \times $ curvature condition, which both amount to checking for the strict positivity of quantities defined by simple formulas in terms of arc length, tangent vectors, and radii of curvature along all paths of $\mathcal{P}$. An application to the study of wellposedness and local minima of a nonlinear least squares problem is given.en
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol29en
dc.relation.isversionofjnlissue6en
dc.relation.isversionofjnldate1991
dc.relation.isversionofjnlpages1348-1372en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/0329069en
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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