Hausdorff Matching and Lipschitz Optimization

In this paper, we prove the Lipschitz continuity with respect to the Hausdorff metric of some parametrized families of sets in R³. This implies that many Hausdorff approximation (Hausdorff matching) problems can be reduced to searching a global minimum of a real Lipschitz function of real variables. Practical methods are presented for obtaining reduced search spaces for these minimization problems.