A Characterization by Optimization of the Monge Point of a Tetrahedron

作者：Hadjisavvas Nicolas; Hiriart Urruty Jean Baptiste^*; Laurent Pierre Jean

来源：Journal of Optimization Theory and Applications, 2016, 171(3): 856-864.

DOI：10.1007/s10957-014-0684-6

• Tetrahedron
• Monge point
• Quadratic convex function
• Variational principle

" nihil omnino in mundo contingint, in quo non maximi minimive ratio quapiam eluceat", translated into " 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.

• 出版日期2016-12