Local Lipschitz-constant functions and maximal subdifferentials

Title: Local Lipschitz-constant functions and maximal subdifferentials
Creator: Borwein, J. M.; Vanderwerff, J.; Wang, Xianfu
Relation: Set-Valued and Variational Analysis Vol. 11, Issue 1, p. 37-67
Publisher Link: http://dx.doi.org/10.1023/A:1021975622768
Publisher: Springer
Resource Type: journal article
Date: 2003
Description: It is shown that if k(x) is an upper semicontinuous and quasi lower semicontinuous function on a Banach space X, then k(x)B_X* is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its ‘local Lipschitz-constant’ function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed.
Subject: Lipschitz function; Baire category; Clarke subdifferential; approximate subdifferential; local Lipschitz-constant function
Identifier: http://hdl.handle.net/1959.13/940681
Identifier: uon:13079
Identifier: ISSN:1877-0533
Language: eng
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