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Quasi-convex sets and size × curvature condition, application to nonlinear inversion

Chavent, Guy (1991), Quasi-convex sets and size × curvature condition, application to nonlinear inversion, Applied Mathematics and Optimization, 24, 1, p. 129-169. http://dx.doi.org/10.1007/BF01447739

Type
Article accepté pour publication ou publié
Date
1991
Journal name
Applied Mathematics and Optimization
Volume
24
Number
1
Publisher
Springer
Pages
129-169
Publication identifier
http://dx.doi.org/10.1007/BF01447739
Metadata
Show full item record
Author(s)
Chavent, Guy
Abstract (EN)
We define a family of sets of a Hilbert space (“quasi-convex sets”) on which a generalization of the usual theory of projection on convex sets can be defined (existence, uniqueness, and stability of the projection of all points of some neighborhood of the set). We then give a constructive sufficient condition, called the size × curvature condition, for a setD to be quasi-convex, which involves radii of curvatures of curves lying on the setD. Finally, we use the above result for the study of nonlinear least-squares problems, as they appear in parameter estimation, for which we give a sufficient condition ensuring existence, uniqueness, and stability.
Subjects / Keywords
nonlinear least-squares problems; Hilbert space

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