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

Chavent, Guy

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

Number

Publisher

Springer

Pages

129-169

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