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New interval methods for constrained global optimization

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Abstract

Interval analysis is a powerful tool which allows to design branch-and-bound algorithms able to solve many global optimization problems. In this paper we present new adaptive multisection rules which enable the algorithm to choose the proper multisection type depending on simple heuristic decision rules. Moreover, for the selection of the next box to be subdivided, we investigate new criteria. Both the adaptive multisection and the subinterval selection rules seem to be specially suitable for being used in inequality constrained global optimization problems. The usefulness of these new techniques is shown by computational studies.

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Authors and Affiliations

  1. Research Group on Artificial Intelligence of the Hungarian Academy of Sciences, University of Szeged, Hungary

    M.Cs. Markót

  2. Advanced Concepts Team, European Space Agency, ESTEC, EUIP, Keplerlaan 1, 2201, AZ, Noordwijk, The Netherlands

    M.Cs. Markót

  3. Department of Statistics and Operations Research, University of Murcia, Spain

    J. Fernández

  4. Department of Computer Architecture and Electronics, University of Almería, Spain

    L.G. Casado

  5. Institute of Informatics, University of Szeged, Hungary

    T. Csendes

Authors
  1. M.Cs. Markót
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  2. J. Fernández
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  3. L.G. Casado
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  4. T. Csendes
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Correspondence to M.Cs. Markót.

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Markót, M., Fernández, J., Casado, L. et al. New interval methods for constrained global optimization. Math. Program. 106, 287–318 (2006). https://doi.org/10.1007/s10107-005-0607-2

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  • DOI: https://doi.org/10.1007/s10107-005-0607-2

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