Ample Parameterization of Variational Inclusions

For a general category of variational inclusions in finite dimensions, a class of parameterizations, called "ample" parameterizations, is identified that is rich enough to provide a full theory of Lipschitz-type properties of solution mappings without the need to resort to the auxiliary introduction of canonical parameters. Ample parameterizations also support a detailed description of the graphical geometry that underlies generalized differentiation of solutions mappings. A theorem on proto-derivatives is thereby obtained. The case of a variational inequality over a polyhedral convex set is given special treatment along with an application to minimizing a parameterized function over such a set.