- 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
- Reviewed
- Hits: 2812
- Visitors: 3387
- Downloads: 0
Thumbnail | File | Description | Size | Format |
---|