On a generic class of regular one-parametric variational inequalities

Abstract

In this paper the regularity of one-parametric opitmization problems in the sense of Jongen, Jonker and Twilt is extended to one-parametric variational inequalities. The five singularities are defined in this context and suitable indices are described around 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 inequalties is proved and a corresponding linear quadratic perturbation result is stated.