Geodesic
Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials
Serdica Mathematical Journal, Tome 35 (2010) no. 4, pp. 387-402

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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.
Keywords: Lower Semicontinuous Function, Inf-convolution, Subdifferential, Approximate Sum Rule, Asplund Space, Subdifferentiability Space, Trustworthy Space, Variational Analysis 
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     title = {Dense {Subdifferentiability} and {Trustworthiness} for {Arbitrary} {Subdifferentials}},
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Jules, Florence; Lassonde, Marc. Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials. Serdica Mathematical Journal, Tome 35 (2010) no. 4, pp. 387-402. http://geodesic.mathdoc.fr/item/SMJ2_2010_35_4_a3/