Bisection method in higher dimensions

G. R. Wood*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    Is the familiar bisection method part of some larger scheme? The aim of this paper is to present a natural and useful generalisation of the bisection method to higher dimensions. The algorithm preserves the salient features of the bisection method: it is simple, convergence is assured and linear, and it proceeds via a sequence of brackets whose infinite intersection is the set of points desired. Brackets are unions of similar simplexes. An immediate application is to the global minimisation of a Lipschitz continuous function defined on a compact subset of Euclidean space.

    Original languageEnglish
    Pages (from-to)319-337
    Number of pages19
    JournalMathematical Programming, Series A
    Volume55
    Issue number3
    Publication statusPublished - 6 Jul 1992

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