Regular Points of Lipschitz Functions

Let f be a locally Lipschitz function on a Banach space X, and S a subset of X. We define regular (i.e. noncritical) points for f relative to S, and give a sufficient condition for a point $z \in S$ to be regular. This condition is then expressed in the particular case when f is ${C^1}$, and is used to obtain a new proof of Hoffman’s inequality in linear programming.