• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

New Size x Curvature Conditions for Strict Quasiconvexity of Sets

Thumbnail
Date
1991
Dewey
Probabilités et mathématiques appliquées
Sujet
projection theory; approximation theory; nonlinear least squares; inverse problems
Journal issue
SIAM Journal on Control and Optimization
Volume
29
Number
6
Publication date
1991
Article pages
1348-1372
Publisher
SIAM
DOI
http://dx.doi.org/10.1137/0329069
URI
https://basepub.dauphine.fr/handle/123456789/14104
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Chavent, Guy
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.