Abstract
It is known that a locally Lipschitz continuous function ƒ: R n → R n which is strongly B-differentiable at a point x 0 ∈ 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.
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