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Convex Maximization Formulation of General Sphere Packing Problem
2020
Journal:  
The Bulletin of Irkutsk State University Series Mathematics
Author:  
Abstract:

We consider a general sphere packing problem which is to pack nonoverlapping 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.

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2020
Journal:  
The Bulletin of Irkutsk State University Series Mathematics
Author:  
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The Bulletin of Irkutsk State University Series Mathematics

Field :   Fen Bilimleri ve Matematik

Journal Type :   Uluslararası

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Article : 601
Cite : 1
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The Bulletin of Irkutsk State University Series Mathematics