On using estimates of Lipschitz constants in global optimization. Hansen, P., Jaumard, B., & Lu, S. H. Journal of Optimization Theory and Applications, 75(1):195–200, Oct, 1992.
On using estimates of Lipschitz constants in global optimization [link]Paper  doi  abstract   bibtex   
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.
@Article{Hansen1992,
    author      = {Hansen, P. and Jaumard, B. and Lu, S. H.},
    title       = {On using estimates of Lipschitz constants in global optimization},
    doi         = {10.1007/BF00939912},
    issn        = {1573-2878},
    journal     = {Journal of Optimization Theory and Applications},
    month       = {Oct},
    number      = {1},
    pages       = {195--200},
    url         = {https://doi.org/10.1007/BF00939912},
    volume      = {75},
    year        = {1992},
    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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