Geodesic
Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 142-155

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The problem of finding the optimal location of moving bodies in three-dimensional Euclidean space is considered. We study the problem of finding such a position for two given polytopes $ A $ and $ B $ at which the Hausdorff distance between them would be minimal. To solve it, the apparatus of convex and nonsmooth analysis is used, as well as methods of computational geometry. Iterative algorithms have been developed and justification has been made for the correctness of their work. A software package has been created, its work is illustrated with specific examples.
Mots-clés : Hausdorff distance
Keywords: minimization, subdifferential, Chebyshev center. 
@article{IIMI_2021_57_a5,
     author = {P. D. Lebedev and A. A. Uspenskii and V. N. Ushakov},
     title = {Iterative algorithms for minimizing the {Hausdorff} distance between convex polyhedrons},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {142--155},
     publisher = {mathdoc},
     volume = {57},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_57_a5/}
}
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P. D. Lebedev; A. A. Uspenskii; V. N. Ushakov. Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 142-155. http://geodesic.mathdoc.fr/item/IIMI_2021_57_a5/