Mathematical Programming

, Volume 55, Issue 1, pp 319-337

First online:

The bisection method in higher dimensions

  • G. R. WoodAffiliated withMathematics Department, University of Canterbury

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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.

AMS 1980 Subject Classification


Key words

Bisection simplex global optimisation linear convergence zonotope tiling