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The bisection method in higher dimensions

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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.

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Wood, G.R. The bisection method in higher dimensions. Mathematical Programming 55, 319–337 (1992). https://doi.org/10.1007/BF01581205

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  • DOI: https://doi.org/10.1007/BF01581205

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