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On using estimates of Lipschitz constants in global optimization

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Abstract

Several authors have proposed estimating Lipschitz constants in global optimization by a multiple of the largest slope (in absolute value) between successive evaluation points. A class of univariate functions is exhibited for which the global optimum will be missed when using such a procedure, even if the multiple is arbitrarily large.

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Author information

Authors and Affiliations

  1. GERAD and École des Hautes Études Commerciales, Montréal, Quebec, Canada

    P. Hansen (Professor) & B. Jaumard (Assistant Professor)

  2. PSEG, Newark, New Jersey

    S. H. Lu (Staff Member)

Authors
  1. P. Hansen
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  2. B. Jaumard
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  3. S. H. Lu
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Additional information

Communicated by D. F. Shanno

Research of the first and third authors was supported by AFOSR Grants 0271 and 0066 to Rutgers University. Research of the second author was supported by NSERC Grant GP0036426 and FCAR Grant 90NC0305.

This research was done while the first author was Professor and the third author was Graduate Student at RUTCOR, Rutgers University.

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Hansen, P., Jaumard, B. & Lu, S.H. On using estimates of Lipschitz constants in global optimization. J Optim Theory Appl 75, 195–200 (1992). https://doi.org/10.1007/BF00939912

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  • DOI: https://doi.org/10.1007/BF00939912

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