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.