Some Properties and Applications of the Hausdorff Distance

Some properties of Hausdorff distance are studied. It is shown that, in every infinite-dimensional normed space, there exists a pair of closed and bounded sets such that the distance between every two points of these sets is greater than the Hausdorff distance between these sets. A relation of the obtained result to set-valued analysis is discussed. © 2015, Springer Science+Business Media New York.

Authors
Arutyunov A.V. 1 , Vartapetov S.A.2 , Zhukovskiy S.E. 1
Journal
Journal of Optimization Theory and Applications
Publisher
Kluwer Academic Publishers-Plenum Publishers
Number of issue
2
Language
English
Pages
527-535
Status
Published
Link
External link
DOI
10.1007/S10957-015-0732-X
Volume
171
Year
2016
Organizations
  • 1 Peoples’ Friendship University of Russia, Miklukho-Maklaya Str., 6, Moscow, 117198, Russian Federation
  • 2 Faculty of Computational Mathematics and Cybernetics, Moscow State University, GSP-1, 1-52, Leninskiye Gory, Moscow, 119991, Russian Federation
Keywords
Hausdorff metric; Lipschitz continuity; Orthogonality in a normed space
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