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On the uniqueness of local minima for general abstract nonlinear least-squares problems

dc.contributor.authorChavent, Guy
dc.date.accessioned2014-10-30T13:47:14Z
dc.date.available2014-10-30T13:47:14Z
dc.date.issued1988
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14098
dc.language.isoenen
dc.subjectPDEen
dc.subject.ddc515en
dc.titleOn the uniqueness of local minima for general abstract nonlinear least-squares problemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe effectiveness of the inversion of a mapping phi defined on a set C by nonlinear least-squares techniques relies on, among other things, the uniqueness of local minima of the least-squares criterion, which ensures that the numerical optimisation algorithm (if they do) converges towards the global minimum of the least-squares functional. The author defines a number y depending only on C and phi which, if the size of phi (C) is not too large with respect to its curvature, is strictly positive, thus yielding the uniqueness of all local minima having a value smaller than y. The condition y>0 requires neither convexity of C nor any monotonic property of phi , but involves the computation of an infimum over delta C* delta C of first and second derivatives of phi . Numerical applications to the estimation of two parameters in a parabolic equation are given.en
dc.relation.isversionofjnlnameInverse Problems
dc.relation.isversionofjnlvol4en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate1988
dc.relation.isversionofdoihttp://dx.doi.org/10.1088/0266-5611/4/2/007en
dc.relation.isversionofjnlpublisherIOPen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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