Clarke critical values of subanalytic Lipschitz continuous functions

Jérôme Bolte, et al. "Clarke critical values of subanalytic Lipschitz continuous functions." Annales Polonici Mathematici 87.1 (2005): 13-25. <http://eudml.org/doc/281075>.

@article{JérômeBolte2005,
abstract = {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.},
author = {Jérôme Bolte, Aris Daniilidis, Adrian Lewis, Masahiro Shiota},
journal = {Annales Polonici Mathematici},
keywords = {Clarke critical point; convex-stable subdifferential; nonsmooth analysis; Morse-Sard theorem; subanalytic function},
language = {eng},
number = {1},
pages = {13-25},
title = {Clarke critical values of subanalytic Lipschitz continuous functions},
url = {http://eudml.org/doc/281075},
volume = {87},
year = {2005},
}

TY - JOUR
AU - Jérôme Bolte
AU - Aris Daniilidis
AU - Adrian Lewis
AU - Masahiro Shiota
TI - Clarke critical values of subanalytic Lipschitz continuous functions
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 13
EP - 25
AB - 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.
LA - eng
KW - Clarke critical point; convex-stable subdifferential; nonsmooth analysis; Morse-Sard theorem; subanalytic function
UR - http://eudml.org/doc/281075
ER -