On Characterizations of Submanifolds via Smoothness of the Distance Function in Hilbert Spaces

David Salas () and Lionel Thibault ()
Additional contact information
David Salas: Universidad de O’Higgins
Lionel Thibault: Université de Montpellier

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 9, 189-210

Abstract: Abstract The property of continuous differentiability with Lipschitz derivative of the square distance function is known to be a characterization of prox-regular sets. We show in this paper that the property of higher-order continuous differentiability with locally uniformly continuous last derivative of the square distance function near a point of a set characterizes, in Hilbert spaces, that the set is a submanifold with the same differentiability property near the point.

Keywords: Submanifolds; Distance function; Metric projection; Local uniform continuity; Diffeomorphism; Prox-regular set; Hilbert space; 53B25; 49J50; 41A65; 58C20; 46C05 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01473-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-019-01473-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01473-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().