Some equivalent variational principles for
viscosity subderivatives with controlled ranks
J. Borwein, B. Mordukhovich, and Y. Shao
ABSTRACT.
We establish an enhanced fuzzy sum rule for (viscosity)
$\beta$-subderivatives with controlled ranks (Lipschitz constants). This
rule is shown to be equivalent to a variant
of the smooth variational principle and to a nonconvex separation
theorem formulated in terms of the (viscosity) $\beta$-normals with
controlled ranks (in $\beta$-smooth spaces). This fuzzy sum rule is then
used to provide a
simplified proof for the sequential representation of the
geometric normal cone recently established by Borwein and Ioffe.