Genericity and Holder Stability in Semi-Algebraic Variational Inequalities

The aim of this paper is twofold. We first present generic properties of semi-algebraic variational inequalities: typical semi-algebraic variational inequalities have finitely many solutions, around each of which they admit a unique active manifold and such solutions are nondegenerate. Second, based on these results, we offer Holder stability, upper semi-continuity, and lower semi-continuity properties of the solution map of parameterized variational inequalities.