upper semidifferentiable functions?

Hi all,

I am an engineering student learning some nonsmooth optimization stuff
now.
I have doubts of this semismoothness defintion introduced by A.
Bihain:

***definition of semismooth:
a locally Lipschitz functin f: R^n -> R is called upper
semidifferentiable at x \in R^n iff
for all d \in R^n and for all sequence {t_k} \subset R_+, and {g_k}
\subset R^n,
with {t_k} -> 0 and g_k \in \partial f(x+t_k*d), there is a sequence
of positive
integers K \subset N, such that
lim_{k _> \infinity, k \in K} {[f(x+t_k*d) - f(x)]/g_k - <g_k, d> } <=
0.

Can anyone give me a geometric description sbout this definition?
I can not understand it well.

***Can we prove that a piecewise linear function f:R^n -> R,
which is continous and locally Liptschitz, is upper
semidifferentiable?
I guess it is but I have no idea how to prove it.

Thanks a lot,
Beet

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