Lipschitzian multifunctions and a Lipschtzian inverse mapping theorem

We introduce a new class of multifunctions whose graphs under certain "kern el inverting" matrices, are locally equal to the graphs of Lipschitzian (si ngle-valued) mappings. We characterize the existence of Lipschitzian locali zations of these multifunctions in terms of a natural condition on a genera lized Jacobian mapping. One corollary to our main result is a Lipschitzian inverse map ping theorem for the broad class of "max hypomonotone" multifun ctions. We apply our theoretical results to the sensitivity analysis of sol ution mappings associated with parameterized optimization problems. In part icular, we obtain new characterizations of the Lipschitzian stability of st ationary points and Karush-Kuhn-Tucker pairs associated with parameterized nonlinear programs.