The bisection method in higher dimensions

The bisection method in higher dimensions

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Article ID: iaor1993784
Country: Netherlands
Volume: 55
Issue: 3
Start Page Number: 319
End Page Number: 337
Publication Date: Jul 1992
Journal: Mathematical Programming (Series A)
Authors:
Keywords: computational analysis
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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