Optimal Control Sphere Packing Problem

Authors

  • Rentsen Enkhbat Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar 13330, Mongolia

DOI:

https://doi.org/10.5564/mmj.v26i24.3001

Keywords:

Sphere packing problem, optimal control, phase and control constraints, Malfatti’s problem

Abstract

The sphere packing problem which is to pack non-overlapping spheres with the maximum volume into a convex set. The problem belongs to a class of global optimization. Convex maximization formulation of the problem is given in [1, 12]. In this paper, we formulate a new optimal control problem based on the sphere packing problem which is a nonconvex optimal control problem with phase and control constraints. A discrete version of the new optimal control problem for sphere packing problem has been
discussed. We examine also Malfatti’s problem [17] from a view point of optimal control theory.

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Published

2023-08-31

How to Cite

Enkhbat, R. (2023). Optimal Control Sphere Packing Problem. Mongolian Mathematical Journal, 26(24), 17–23. https://doi.org/10.5564/mmj.v26i24.3001

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