Effect of dimensionality on the Nelder–Mead simplex method

Abstract

Abstract The effect of dimensionality on the widely used Nelder–Mead simplex method for unconstrained optimization is investigated. It is shown that by using the quadratic function f(x)=x T x, the Nelder–Mead simplex method deteriorates as the dimension increases. Keywords: Nelder–Mead methodSimplexEffect of dimensionalityConvergenceOptimization Acknowledgements We are very grateful to the referees for their insightful and constructive comments and suggestions, which helped us to improve the content and presentation of the paper. We also thank David Byatt for providing us his thesis. Lixing Han's research was supported in part by a UM-Flint 2002 summer research fellowship. The work of this Michael Neumann was supported in part by NSF Grant No. DMS9973247.