K.I.M. McKinnon
Technical Report MS 96-006
Abstract
This paper analyses the behaviour of the Nelder-Mead simplex method for
a family of examples which cause the method to converge to a
non-stationary point. All the examples use continuous functions
of two variables. The family of functions contains strictly convex
functions with up to three continuous derivatives. In all the examples
the method repeatedly applies the inside contraction step with the best
vertex remaining fixed. The simplices tend to a straight line which is
orthogonal to the steepest descent direction. It is shown that this
behaviour cannot occur for functions with more than three continuous
derivatives. The stability of the examples is analysed.
Key words: Nelder-Mead method, direct search, simplex, unconstrained minimization
amsmos: 65K05