Geodesic
Convex maximization formulation of general sphere packing problem
The Bulletin of Irkutsk State University. Series Mathematics, Tome 31 (2020), pp. 142-149

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a general sphere packing problem which is to pack non-overlapping spheres (balls) with the maximum volume into a convex set. This problem has important applications in science and technology. We prove that this problem is equivalent to the convex maximization problem which belongs to a class of global optimization. We derive necessary and sufficient conditions for inscribing a finite number of balls into a convex compact set. In two dimensional case, the sphere packing problem is a classical circle packing problem. We show that 200 years old Malfatti's problem [11] is a particular case of the circle packing problem. We also survey existing algorithms for solving the circle packing problems as well as their industrial applications.
Keywords: sphere packing problem, convex maximization, optimality conditions
Mots-clés : Malfatti's problem. 
@article{IIGUM_2020_31_a9,
     author = {R. Enkhbat},
     title = {Convex maximization formulation of general sphere packing problem},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {142--149},
     publisher = {mathdoc},
     volume = {31},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2020_31_a9/}
}
TY  - JOUR
AU  - R. Enkhbat
TI  - Convex maximization formulation of general sphere packing problem
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2020
SP  - 142
EP  - 149
VL  - 31
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2020_31_a9/
LA  - en
ID  - IIGUM_2020_31_a9
ER  - 
%0 Journal Article
%A R. Enkhbat
%T Convex maximization formulation of general sphere packing problem
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2020
%P 142-149
%V 31
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2020_31_a9/
%G en
%F IIGUM_2020_31_a9
R. Enkhbat. Convex maximization formulation of general sphere packing problem. The Bulletin of Irkutsk State University. Series Mathematics, Tome 31 (2020), pp. 142-149. http://geodesic.mathdoc.fr/item/IIGUM_2020_31_a9/