Approximate values for mathematical programs with variational inequality constraints

In general the infimal value of a mathematical program with variational inequality constraints (MPVI) is not stable under perturbations in the sense that the sequence of infimal values for the perturbed programs may not converge to the infimal value of the original problem even in presence of nice data. Thus, for these programs different types of values, which approximate the exact value from below or/and from above, are considered under or without perturbations