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Title: Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials
Authors: Jules, Florence
Lassonde, Marc
Keywords: Lower Semicontinuous Function
Approximate Sum Rule
Asplund Space
Subdifferentiability Space
Trustworthy Space
Variational Analysis
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 4, (2010), 387p-402p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.
ISSN: 1310-6600
Appears in Collections:Volume 36, Number 4

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