  We consider algorithms that, from an arbitrarily sampling of $N$ spheres
(possibly overlapping), find a close packed configuration 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.
