Nondegeneracy Concepts for Zeros of Piecewise Smooth Functions

A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fréchet differentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational inequality problem corresponding to a polyhedral convex set. Some properties of nondegenerate zeros of piecewise affine functions are described. We generalize a recent result of Ferris and Pang on the existence of a nondegenerate solution of an affine variational inequality problem which itself is a generalization of a theorem of Goldman and Tucker.