# Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

Jules, Florence; Lassonde, Marc

Serdica Mathematical Journal (2010)

- Volume: 35, Issue: 4, page 387-402
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topJules, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.