- Title
- Epi-Lipschitz-like sets in Banach space: theorems and examples
- Creator
- Borwein, Jonathan Michael
- Relation
- Nonlinear Analysis: Theory, Methods & Applications Vol. 11, Issue 10, p. 1207-1217
- Publisher Link
- http://dx.doi.org/10.1016/0362-546X(87)90008-3
- Publisher
- Pergamon
- Resource Type
- journal article
- Date
- 1987
- Description
- One can, following Rockafellar, define generalized derivatives of arbitrary functions on arbitrary topological vector spaces. In this generality, only a few relatively unrefined results can be established. These results typically do not recapture much of the detailed information available in Rn or for Lipschitz functions. To obtain more delicate results it is necessary to restrict either the spaces or the functions. Many examples are available in Borwein and Strojwas which illustrate how badly wrong things may go outside of a Baire metrizable or Banach space setting. In this paper we restrict our attention primarily to a Banach space X and consider what properties a set C in X should have for the Clarke tangent cone Tc(x) and normal cone Nc(x) to adequately measure boundary behaviour of x in C.
- Subject
- nonsmooth analysis; Lipschitz-like functions; epi-Lipschitz-like sets; normal cones; non-support points; differential inclusions; locally compact subgradients
- Identifier
- http://hdl.handle.net/1959.13/941050
- Identifier
- uon:13165
- Identifier
- ISSN:0362-546X
- Language
- eng
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