Lipschitz functions with prescribed derivatives and subderivatives

Title: Lipschitz functions with prescribed derivatives and subderivatives
Creator: Borwein, Jonathan M.; Moors, Warren B.; Wang, Xianfu
Relation: Nonlinear Analysis: Theory, Methods & Applications Vol. 29, Issue 1, p. 53-63
Publisher Link: http://dx.doi.org/10.1016/S0362-546X(96)00050-8
Publisher: Pergamon
Resource Type: journal article
Date: 1997
Description: It is natural to ask when a given set-valued mapping T, which maps from a nonempty open subset U of a Banach space X into subsets of its dual, is the Clarke subdifferential mapping of some real-valued locally Lipschitz functions defined on U. In the case when X = R and U is an open interval the answer is known (see [l]). However, the general question still remains. Even the simpler question of how to construct nontrivial Lipschitz functions which are not built-up from either convex or distance functions has yet to be satisfactorily resolved. In this paper we present a technique for constructing such real-valued locally Lipschitz functions defined on separable Banach spaces. Using this construction we are able to recreate many known examples of pathological locally Lipschitz functions.
Subject: Lipschitz functions; differentiability; Clarke subgradient; minimal cusco; Haar null set; maximal cyclically monotone operator
Identifier: http://hdl.handle.net/1959.13/1046791
Identifier: uon:14689
Identifier: ISSN:0362-546X
Language: eng
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