Approximate Subgradients and Coderivatives in Rn
نویسنده
چکیده
We show that in two dimensions or higher, the Mordukhovich-loffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Frechet 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 FrCchet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the MordukhovichIoffe coderivative can be almost everywhere disconnected. Mathematics Subject Classifications (1991). Primary 49552, Secondary 26A27, 26B12, 49550, 52A20.
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