Stability of regularized bilevel programming problems

A bilevel programming problem S is considered. First, sufficient conditions of minimal character are given on the data of the problem in order to guarantee the lower semicontinuity of the marginal function of the upper level problem. Then, for epsilon > 0, a regularized problem S(epsilon) is considered for which continuity of the regularized marginal function and convergence of the approximate value, as epsilon goes to zero, are obtained. Moreover, under perturbations on the data, convergence results for the perturbed marginal functions and the solutions to the problem S-n(epsilon) are given for any epsilon > 0.