Mathematical programs with complementarity constraints: Convergence properties of a smoothing method

In this paper, optimization problems P with complementarity constraints are considered. Characterizations for local minimizers (x) over bar of P of Orders 1 and 2 are presented. We analyze a parametric smoothing approach for solving these programs in which P is replaced by a perturbed problem P-tau depending on a (small) parameter tau. We are interested in the convergence behavior of the feasible set F-tau and the convergence of the solutions (x) over bar (7) of P-tau for tau -> 0. In particular, it is shown that, under generic assumptions, the solutions (x) over bar (tau) are unique and converge to a solution (x) over bar of P with a rate O(root tau). Moreover, the convergence for the Hausdorff distance d(F-tau, F) between the feasible sets of P-tau and P is of order O(root tau).