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