We consider algorithms that, from an arbitrarily sampling of
N
spheres
(possibly overlapping), nd a close packed con guration without overlapping.
These problems can be formulated as minimization problems with non-convex
constraints. For such packing problems, we observe that the classical iterative
Arrow-Hurwicz algorithm does not converge. We derive a novel algorithm
from a multi-step variant of the Arrow-Hurwicz scheme with damping. We
compare this algorithm with classical algorithms belonging to the class of
linearly constrained Lagrangian methods and show that it performs better.
We provide an analysis of the convergence of these algorithms in the simple
case of two spheres in one spatial dimension. Finally, we investigate the
behaviour of our algorithm when the number of spheres is large in two and
three spatial dimensions.