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Some Properties and Applications of the Hausdorff Distance

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Abstract

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.

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Acknowledgments

The investigation is performed in the framework of state assignment of Ministry of Education and Science of Russian Federation in the field of scientific activity implementation, Project No. 1.333.2014/K. The investigation is also supported by the RFBR Grant, Project No. 14-01-31185, and by the Grant of the President of the Russian Federation, Project No. MK-5333.2015.1.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Miklukho-Maklaya Str., 6, Moscow, 117198, Russia

    A. V. Arutyunov & S. E. Zhukovskiy

  2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, GSP-1, 1-52, Leninskiye Gory, Moscow, 119991, Russia

    S. A. Vartapetov

Authors
  1. A. V. Arutyunov
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  2. S. A. Vartapetov
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  3. S. E. Zhukovskiy
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Corresponding author

Correspondence to S. E. Zhukovskiy.

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Communicated by Boris S. Mordukhovich.

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Arutyunov, A.V., Vartapetov, S.A. & Zhukovskiy, S.E. Some Properties and Applications of the Hausdorff Distance. J Optim Theory Appl 171, 527–535 (2016). https://doi.org/10.1007/s10957-015-0732-x

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  • DOI: https://doi.org/10.1007/s10957-015-0732-x

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