  In these notes, we present a general result concerning the Lipschitz
regularity of a certain type of set-valued maps often found in constrained
optimization and control problems. The class of multifunctions examined in this
paper is characterized by means of a set of Lipschitz continuous constraint
functions defined on some Lipschitz manifold. The proof of the regularity
result for this class of multifunctions is based on a quantitative version of
the Implicit Function Theorem for Lipschitzian maps which provides estimates
for the neighborhoods where the implicit map can be defined.
