Optimal Control Sphere Packing Problem - Enkhbat, Rentsen (Mongolian Mathematical Journal, 2023)
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.