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Steiner's problem and fagnano's result on the sphere

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Abstract

This note describes the nature of optimal solutions for the spherical Steiner-Weber location problem for the case of unit weights and either 3 or 4 demand points (requireing 4 demand points to lie in an open hemisphere). Geometrically appealing results which are necessary conditions for optimum solutions and spherical analogs of known planar results are obtained.

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Authors and Affiliations

  1. United States Air Force Academy, Colorado Springs, CO, USA

    Daniel W. Litwhiler

  2. University of Oklahoma, Norman, OK, USA

    Adel A. Aly

Authors
  1. Daniel W. Litwhiler
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  2. Adel A. Aly
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Litwhiler, D.W., Aly, A.A. Steiner's problem and fagnano's result on the sphere. Mathematical Programming 18, 286–290 (1980). https://doi.org/10.1007/BF01588324

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  • DOI: https://doi.org/10.1007/BF01588324

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