The bisection method in higher dimensions
- G. R. Wood
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- Patricio Basso, “Iterative methods for the localization of the global maximum,”SIAM Journal on Numerical Analysis 19 (1982) 781–792.
- Gustave Choquet,Lectures on Analysis, Vol. 1 (Benjamin, New York, 1969).
- A. Eiger, K. Sikorski and F. Stenger, “A bisection method for systems of nonlinear equations,”ACM Transactions on Mathematical Software 10 (1984) 367–377.
- P. McMullen, “Space tiling zonotopes,”Mathematika 22 (1975) 202–211.
- Regina Hunter Mladineo, “An algorithm for finding the global maximum of a multimodal, multivariate function,”Mathematical Programming 34 (1986) 188–200.
- S.A. Piyavskii, “An algorithm for finding the absolute extremum of a function,”USSR Computational Mathematics and Mathematical Physics 12 (1972) 57–67.
- J.E. Dennis Jr. and Robert B. Schnabel,Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983).
- Bruno O. Shubert, “A sequential method seeking the global maximum of a function,”SIAM Journal on Numerical Analysis 9 (1972) 379–388.
- G.R. Wood, “On computing the dispersion function,”Journal of Optimization Theory and Applications 58 (1988) 331–350.
- G.R. Wood, “Multidimensional bisection applied to global optimisation,”Computers and Mathematics with Applications 21 (1991) 161–172.
- The bisection method in higher dimensions
Volume 55, Issue 1-3 , pp 319-337
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- global optimisation
- linear convergence
- Industry Sectors
- G. R. Wood (1)
- Author Affiliations
- 1. Mathematics Department, University of Canterbury, Christchurch, New Zealand