On a generic class of regular one-parametric variational inequalities

In this paper the regularity of one-parametric optimization problems in the sense of Jongen, Jonker and Twilt is extended to one-parametric variational inequalities. There are five different types of singularities in this context. Suitable indices are introduced to describe them. Many of the local properties of the singularities are also proved for this case. The generic property of the defined class of regular one-parametric variational inequalities is proved and a corresponding linear quadratic perturbation result is stated.