In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space are introduced. Two different models 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.
CITATION STYLE
Birgin, E. G., Lobato, R. D., & Martínez, J. M. (2016). Packing ellipsoids by nonlinear optimization. Journal of Global Optimization, 65(4), 709–743. https://doi.org/10.1007/s10898-015-0395-z
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