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Global optimization of Hölder functions |
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| Authors: | Eric Gourdin Brigitte Jaumard Rachid Ellaia |
| Affiliation: | (1) Department of Mathematics and Industrial Engineering, Ecole Polytechnique de Montréal, Station “Centre-ville”, P.O. Box 6079, H3C 3A7 Montréal, Québec, Canada;(2) Ecole Polytechnique de Montréal, GERAD, Station “Centre-ville”, P.O. Box 6079, H3C 3A7 Montréal, Québec, Canada;(3) Department of Mathematics and Industrial Engineering, Station “Centre-ville”, P.O. Box 6079, H3C 3A7 Montréal, Québec, Canada;(4) Départmentt E. G.T., Ecole Mohammadia d'Ingénieurs, Avenue Ibn Sina, BP 765, Rabat-Agdal, Maroc |
| 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. |
| Keywords: | Global optimization H?lder functions Lipschitz optimization |
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