Multidimensional bisection

The performance and the context

Zhang Baoping*, G. R. Wood, W. P. Baritompa

*Corresponding author for this work

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    Two aspects of the multidimensional bisection algorithms for the global optimisation of Lipschitz continuous functions are investigated. Firstly, for several test functions we examine the numerical performance of the deepest point algorithm and two acceleration procedures. Secondly, we phrase the branch and bound framework of Horst and Tuy in terms of covers, and show the algorithms to be included in this framework. A result of Basso on the convergence of localisations is extended to higher dimensions.

    Original languageEnglish
    Pages (from-to)337-358
    Number of pages22
    JournalJournal of Global Optimization
    Volume3
    Issue number3
    DOIs
    Publication statusPublished - Sep 1993

    Keywords

    • Bisection
    • branch and bound
    • deterministic
    • global optimisation
    • localisation
    • mathematical programming
    • Mathematics Subject Classifications (1991): 90C30, 65K05
    • numerical performance
    • simplex

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