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: | Wood G.R. |
Keywords: | computational analysis |
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.