A Characterization by Optimization of the Monge Point of a Tetrahedron

Nicolas Hadjisavvas (), Jean-Baptiste Hiriart-Urruty () and Pierre-Jean Laurent ()
Additional contact information
Nicolas Hadjisavvas: University of the Aegean
Jean-Baptiste Hiriart-Urruty: Université Paul Sabatier
Pierre-Jean Laurent: Université Joseph Fourier

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 3, No 5, 856-864

Abstract: 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.

Keywords: Tetrahedron; Monge point; Quadratic convex function; Variational principle; 90C25; 52A20; 52B10 (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-014-0684-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-014-0684-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-014-0684-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().