Packing ellipsoids by nonlinear optimization∗

In this paper, continuous and differentiable nonlinear programming models and algo-rithms for packing ellipsoids in the n-dimensional space are introduced. Two different mod-els for the non-overlapping and models for the inclusion of ellipsoids within half-spaces and ellipsoids are presented. By applying a simple multi-start strategy combined with a clever choice of starting guesses and a nonlinear programming local solver, illustrative numerical experiments are presented. Key words: Cutting and packing ellipsoids, nonlinear programming, models, numerical experiments.