Aubin Criterion for Metric Regularity

We present a derivative criterion for metric regularity of set-valued mappings that is based on works of J.-P. Aubin and co-authors. A related implicit mapping theorem is also obtained. As applications, we first show that Aubin criterion leads directly to the known fact that the mapping describing an equality/inequality system is metrically regular if and only if the Mangasarian-Fromovitz condition holds. We also derive a new necessary and sufficient condition for strong regularity of variational inequalities over polyhedral sets. A new proof of the radius theorem for metric regularity based on Aubin criterion is given as well.