Journal of Global Optimization

, Volume 65, Issue 4, pp 709–743 | Cite as

Packing ellipsoids by nonlinear optimization

  • E. G. Birgin
  • R. D. Lobato
  • J. M. Martínez


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.


Cutting and packing ellipsoids Nonlinear programming Models  Numerical experiments 



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


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • E. G. Birgin
    • 1
  • R. D. Lobato
    • 1
  • J. M. Martínez
    • 2
  1. 1.Department of Computer Science, Institute of Mathematics and StatisticsUniversity of São PauloSão PauloBrazil
  2. 2.Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific ComputingState University of CampinasCampinasBrazil

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