The bisection method in higher dimensions
- G. R. Wood
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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.
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- The bisection method in higher dimensions
Volume 55, Issue 1-3 , pp 319-337
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- global optimisation
- linear convergence
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- G. R. Wood (1)
- Author Affiliations
- 1. Mathematics Department, University of Canterbury, Christchurch, New Zealand