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.
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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