Ill-conditioning has long been regarded as a plague on interior methods, but its damaging effects have rarely been documented. In fact, implementors of interior methods who ignore warnings about the ...
This paper analyzes the behavior of the Nelder--Mead simplex method for a family of examples which cause the method to converge to a nonstationary point. All the examples use continuous functions of ...
You are not logged in to this journal. Log in
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM J. Optim. Volume 9, Issue 1, pp. 112-147 (1998)
Issue Date: 1998
Connotea
CiteULike
del.icio.us
BibSonomy
The Nelder--Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder--Mead algorithm. This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder--Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder--Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.
©1998 Society for Industrial and Applied Mathematics| Permalink: | http://dx.doi.org/10.1137/S1052623496303470 |
KEYWORDS and AMS
PUBLICATION DATA
SIAM