Global optimization of univariate Lipschitz functions: I. Survey and properties. Hansen, P., Jaumard, B., & Lu, S. Mathematical Programming, 55(1):251–272, Apr, 1992.
Paper doi abstract bibtex We consider the following global optimization problems for a univariate Lipschitz functionf defined on an interval [a, b]: Problem P: find a globally optimal value off and a corresponding point; Problem P´x: find a globally$ε$-optimal value off and a corresponding point; Problem Q: localize all globally optimal points; Problem Q´x: find a set of disjoint subintervals of small length whose union contains all globally optimal points; Problem Q\textacutedbl: find a set of disjoint subintervals containing only points with a globally$ε$-optimal value and whose union contains all globally optimal points.
@Article{Hansen1992b,
author = {Hansen, Pierre and Jaumard, Brigitte and Lu, Shi-Hui},
title = {Global optimization of univariate Lipschitz functions: I. Survey and properties},
doi = {10.1007/BF01581202},
issn = {1436-4646},
journal = {Mathematical Programming},
month = {Apr},
number = {1},
pages = {251--272},
url = {https://doi.org/10.1007/BF01581202},
volume = {55},
year = {1992},
abstract = {We consider the following global optimization problems for a univariate Lipschitz functionf defined on an interval [a, b]: Problem P: find a globally optimal value off and a corresponding point; Problem P{\textasciiacutex}: find a globally$\epsilon$-optimal value off and a corresponding point; Problem Q: localize all globally optimal points; Problem Q{\textasciiacutex}: find a set of disjoint subintervals of small length whose union contains all globally optimal points; Problem Q{\textacutedbl}: find a set of disjoint subintervals containing only points with a globally$\epsilon$-optimal value and whose union contains all globally optimal points.}
}
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