dc.contributor.author Chavent, Guy dc.date.accessioned 2014-10-30T14:01:21Z dc.date.available 2014-10-30T14:01:21Z dc.date.issued 1991 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/14104 dc.language.iso en en dc.subject projection theory en dc.subject approximation theory en dc.subject nonlinear least squares en dc.subject inverse problems en dc.subject.ddc 519 en dc.title New Size x Curvature Conditions for Strict Quasiconvexity of Sets en dc.type Article accepté pour publication ou publié dc.description.abstracten Given 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.isversionofjnlname SIAM Journal on Control and Optimization dc.relation.isversionofjnlvol 29 en dc.relation.isversionofjnlissue 6 en dc.relation.isversionofjnldate 1991 dc.relation.isversionofjnlpages 1348-1372 en dc.relation.isversionofdoi http://dx.doi.org/10.1137/0329069 en dc.relation.isversionofjnlpublisher SIAM en dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.relation.forthcoming non en dc.relation.forthcomingprint non en
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