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Global optimization of Hölder functions

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Abstract

We propose a branch-and-bound framework for the global optimization of unconstrained Hölder functions. The general framework is used to derive two algorithms. The first one is a generalization of Piyavskii's algorithm for univariate Lipschitz functions. The second algorithm, using a piecewise constant upper-bounding function, is designed for multivariate Hölder functions. A proof of convergence is provided for both algorithms. Computational experience is reported on several test functions from the literature.

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Authors and Affiliations

  1. Department of Mathematics and Industrial Engineering, Ecole Polytechnique de Montréal, Station “Centre-ville”, P.O. Box 6079, H3C 3A7, Montréal, Québec, Canada

    Eric Gourdin

  2. Ecole Polytechnique de Montréal, GERAD, Station “Centre-ville”, P.O. Box 6079, H3C 3A7, Montréal, Québec, Canada

    Brigitte Jaumard

  3. Department of Mathematics and Industrial Engineering, Station “Centre-ville”, P.O. Box 6079, H3C 3A7, Montréal, Québec, Canada

    Brigitte Jaumard

  4. Départmentt E. G.T., Ecole Mohammadia d'Ingénieurs, Avenue Ibn Sina, BP 765, Rabat-Agdal, Maroc

    Rachid Ellaia

Authors
  1. Eric Gourdin
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  2. Brigitte Jaumard
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  3. Rachid Ellaia
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Gourdin, E., Jaumard, B. & Ellaia, R. Global optimization of Hölder functions. J Glob Optim 8, 323–348 (1996). https://doi.org/10.1007/BF02403997

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  • DOI: https://doi.org/10.1007/BF02403997

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