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Packing ellipsoids by nonlinear optimization

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Abstract

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.

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Acknowledgments

The authors are indebted to the anonymous referees whose comments helped to improve this paper.

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Authors and Affiliations

  1. Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, SP, 05508-090, Brazil

    E. G. Birgin & R. D. Lobato

  2. Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas, Campinas, SP, Brazil

    J. M. Martínez

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  1. E. G. Birgin
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  2. R. D. Lobato
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  3. J. M. Martínez
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Correspondence to R. D. Lobato.

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This work was supported by PRONEX-CNPq/FAPERJ E-26/111.449/2010-APQ1, FAPESP (Grants 2010/10133-0, 2013/03447-6, 2013/05475-7, 2013/07375-0, and 2012/23916-8), and CNPq.

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Birgin, E.G., Lobato, R.D. & Martínez, J.M. Packing ellipsoids by nonlinear optimization. J Glob Optim 65, 709–743 (2016). https://doi.org/10.1007/s10898-015-0395-z

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