Clarke critical values of subanalytic Lipschitz continuous functions

• Autorzy: Jérôme Bolte , Aris Daniilidis , Adrian Lewis , Masahiro Shiota
• Języki publikacji: EN

Abstrakty

EN

The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawłucki's extension of the Puiseux lemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Kategorie tematyczne

• 35B38: Critical points
• 49J52: Nonsmooth analysis

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 87
• Numer: 1
• Strony: 13-25

Daty

wydano

2005

Twórcy

autor

Jérôme Bolte

• Équipe Combinatoire et Optimisation (UMR 7090, Case 189), Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

autor

Aris Daniilidis

• Departament de Matemàtiques, C1/320, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Cerdanyola del Vallès), Spain

autor

Adrian Lewis

• School of Operations Research and Industrial Engineering, Cornell University, 234 Rhodes Hall, Ithaca, NY 14853, U.S.A.

autor

Masahiro Shiota

• Department of Mathematics, Nagoya University (Furocho, Chikusa), Nagoya 464-8602, Japan

Identyfikatory

DOI

10.4064/ap87-0-2