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Damped Arrow-Hurwicz algorithm for sphere packing

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Particle packings are found in a wide range of natural systems, from planet formation or cells in live tissues to the dynamics of crowds of people. The search for packed configurations gives rise to nonconvex optimization problems. These problems become extremely hard as the number of particles increases. In this talk I will derive a novel multi-step variant of the Arrow-Hurwicz algorithm for the packing of N hard-spheres. Numerical results on the convergence time and accuracy will be presented for the case of a global potential acting on a system of N hard-spheres in two spatial dimensions. I will also compare the performance of our method with classical algorithms belonging to the class of linearly constrained Lagrangian methods.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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