Approximate subgradients and coderivatives in R<sup>n</sup>

Title: Approximate subgradients and coderivatives in Rⁿ
Creator: Borwein, D.; Borwein, J. M.; Wang, Xianfu
Relation: Set-Valued Analysis Vol. 4, Issue 4, p. 375-398
Publisher Link: http://dx.doi.org/10.1007/BF00436112
Publisher: Springer
Resource Type: journal article
Date: 1996
Description: We show that in two dimensions or higher, the Mordukhovich-Ioffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Fréchet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich-Ioffe coderivatives. Moreover, the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be nonconvex almost everywhere for Fréchet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be almost everywhere disconnected.
Subject: subgradient; coderivative; generalized Jacobian; Lipschitz function; bump function; guage; nowhere dense set; Lebesgue measure; disconnectedness
Identifier: http://hdl.handle.net/1959.13/940911
Identifier: uon:13131
Identifier: ISSN:0927-6947
Language: eng
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Approximate subgradients and coderivatives in Rn