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A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes

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Abstract

For a given pair of finite point setsP andQ in some Euclidean space we consider two problems: Problem 1 of finding the minimum Euclidean norm point in the convex hull ofP and Problem 2 of finding a minimum Euclidean distance pair of points in the convex hulls ofP andQ. We propose a finite recursive algorithm for these problems. The algorithm is not based on the simplicial decomposition of convex sets and does not require to solve systems of linear equations.

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Authors and Affiliations

  1. Institute of Socio-Economic Planning, University of Tsukuba, 305, Tsukuba, Ibaraki, Japan

    Kazuyuki Sekitani & Yoshitsugu Yamamoto

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  1. Kazuyuki Sekitani
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  2. Yoshitsugu Yamamoto
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Sekitani, K., Yamamoto, Y. A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes. Mathematical Programming 61, 233–249 (1993). https://doi.org/10.1007/BF01582149

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  • DOI: https://doi.org/10.1007/BF01582149

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