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A Characterization by Optimization of the Monge Point of a Tetrahedron

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Abstract

“\(\ldots \) nihil omnino in mundo contingint, in quo non maximi minimive ratio quapiam eluceat”, translated into “\(\ldots \) nothing in all the world will occur in which no maximum or minimum rule is somehow shining forth”, used to say L. Euler in 1744. This is confirmed by numerous applications of mathematics in physics, mechanics, economy, etc. In this note, we show that it is also the case for the classical “centres” of a tetrahedron, more specifically for the so-called Monge point (the substitute of the notion of orthocentre for a tetrahedron). To the best of our knowledge, the characterization of the Monge point of a tetrahedron by optimization, that we are going to present, is new.

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Authors and Affiliations

  1. Department of Product and Systems Design Engineering, University of the Aegean, 84100, Hermoupolis, Syros, Greece

    Nicolas Hadjisavvas

  2. Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 9, France

    Jean-Baptiste Hiriart-Urruty

  3. Laboratoire Jean Kuntzman (LJK), Campus de Saint Martin d’Hères, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Pierre-Jean Laurent

Authors
  1. Nicolas Hadjisavvas
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  2. Jean-Baptiste Hiriart-Urruty
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  3. Pierre-Jean Laurent
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Corresponding author

Correspondence to Jean-Baptiste Hiriart-Urruty.

Additional information

Communicated by Boris S. Mordukhovich.

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Hadjisavvas, N., Hiriart-Urruty, JB. & Laurent, PJ. A Characterization by Optimization of the Monge Point of a Tetrahedron. J Optim Theory Appl 171, 856–864 (2016). https://doi.org/10.1007/s10957-014-0684-6

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  • DOI: https://doi.org/10.1007/s10957-014-0684-6

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