Dense subdifferentiability and trustworthiness for arbitrary subdifferentials

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.
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Submitted on : Friday, May 4, 2012 - 10:46:47 PM
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Florence Jules, Marc Lassonde. Dense subdifferentiability and trustworthiness for arbitrary subdifferentials. Serdica. Mathematical Journal, 2010, 36 (4), pp.387-402. 〈hal-00694603〉

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