The bisection method in higher dimensions

G. R. Wood*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    41 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
    Volume55
    Issue number1-3
    DOIs
    Publication statusPublished - Apr 1992

    Keywords

    • AMS 1980 Subject Classification: 49D37
    • Bisection
    • global optimisation
    • linear convergence
    • simplex
    • tiling
    • zonotope

    Fingerprint

    Dive into the research topics of 'The bisection method in higher dimensions'. Together they form a unique fingerprint.

    Cite this