Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

Jules, Florence, and Lassonde, Marc. "Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials." Serdica Mathematical Journal 35.4 (2010): 387-402. <http://eudml.org/doc/281405>.

@article{Jules2010,
abstract = {2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz Separation property, a strong Compact Separation property and a Minimal property for the analytic approximate subdifferential of Ioffe.},
author = {Jules, Florence, Lassonde, Marc},
journal = {Serdica Mathematical Journal},
keywords = {Lower Semicontinuous Function; Inf-convolution; Subdifferential; Approximate Sum Rule; Asplund Space; Subdifferentiability Space; Trustworthy Space; Variational Analysis; lower semicontinuous function; inf-convolution; subdifferential; approximate sum rule; Asplund space; subdifferentiability space; trustworthy space; variational analysis},
language = {eng},
number = {4},
pages = {387-402},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials},
url = {http://eudml.org/doc/281405},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Jules, Florence
AU - Lassonde, Marc
TI - Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials
JO - Serdica Mathematical Journal
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 4
SP - 387
EP - 402
AB - 2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz Separation property, a strong Compact Separation property and a Minimal property for the analytic approximate subdifferential of Ioffe.
LA - eng
KW - Lower Semicontinuous Function; Inf-convolution; Subdifferential; Approximate Sum Rule; Asplund Space; Subdifferentiability Space; Trustworthy Space; Variational Analysis; lower semicontinuous function; inf-convolution; subdifferential; approximate sum rule; Asplund space; subdifferentiability space; trustworthy space; variational analysis
UR - http://eudml.org/doc/281405
ER -