STRUCTURAL-ANALYSIS OF NONSMOOTH MAPPINGS, INVERSE FUNCTIONS, AND METRIC PROJECTIONS

It is known that a locally Lipschitz continuous function f: R(n) --> R(n) which is strongly B-differentiable at a point x(0) is an element of R(n) is a Lipschitz homeomorphism in a neighborhood of x(0) if and only if its B-derivative at x(0) is a Lipschitz homeomorphism. We show that strongly B-differentiability is a rather restrictive requirement for piecewise differentiable functions. However, it turns out that generically a piecewise differentiable function can be locally transformed into a strongly B-differentiable function by means of a piecewise differentiable homeomorphism. The corresponding criteria yield structural inverse function theorems for piecewise differentiable functions. The results are applied to the metric projection onto a convex set. (C) 1994 Academic Press, Inc.