This paper is a continuation of our previous paper were we presented generalizations of the Dennis-Mor\'e theorem to characterize q-superliner convergences of quasi-Newton methods for solving equations and variational inequalities in Banach spaces. Here we prove Dennis-Mor\'e type theorems for inexact quasi-Newton methods applied to variational inequalities in finite dimensions. We first consider variational inequalities for functions that are merely Lipschitz continuous. Then we present a parallel result for semismooth functions. An erratum to a theorem in our previous paper is also given.
Mathematical Reviews, Ann Arbor, MI 48107-8604, submitted May 7, 2013