Lower Semicontinuous Function Inf-convolution Subdifferential 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.
