A numerical proof by reliable Global Optimization for a problem of covering a rectangle with circles

Sonia Cafieri (1) , Frédéric Messine (2)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 LAPLACE-GREM3 - Groupe de Recherches en Electrodynamique

In this paper, we show how a reliable global Branch and Bound optimization method based on interval arithmetic can be used efficiently to numerically prove a conjecture in geometry about how to cover a rectangle by 6 circles of equal radius.

Mots clés: Reliable Global Optimization; Mathematical Programming; Numerical proof; Covering problem

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]

Sonia Cafieri, Frédéric Messine. A numerical proof by reliable Global Optimization for a problem of covering a rectangle with circles. HUGO 2022 - XV Workshop on Global Optimization, Sep 2022, Szeged, Hungary. ⟨hal-04001679⟩