NONDEGENERACY CONCEPTS FOR ZEROS OF PIECEWISE-SMOOTH FUNCTIONS

A zero of a piecewise smooth function Sis said to be nondegenerate if the function is Frechet differentiable at that point. Using this conce pt, we describe the usual nondegeneracy notions in the settings of non linear (vertical, horizontal, mixed) complementarity problems and the variational inequality problem corresponding to a polyhedral convex se t. Some properties of nondegenerate zeros of piecewise affine function s are described. We generalize a recent result of Ferris and Pang on t he existence of a nondegenerate solution of an affine variational ineq uality problem which itself is a generalization of a theorem of Goldma n and Tucker.