<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically proven convergence properties. The original formulation of the algorithm is stated in R<sup>n</sup> using terms of Euclidean geometry. In this paper we introduce the idea of a hyperbolic variant of this algorithm using the Poincaré disk model of the Bolyai- Lobachevsky geometry. We present a few basic properties of this method and we also give a Matlab implementation in 2 and 3 dimensions</p></abstract>

The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically proven convergence properties. The original formulation of the algorithm is stated in Rn using terms of Euclidean geometry. In this paper we introduce the idea of a hyperbolic variant of this algorithm using the Poincaré disk model of the Bolyai- Lobachevsky geometry. We present a few basic properties of this method and we also give a Matlab implementation in 2 and 3 dimensions

A hyperbolic variant of the Nelder–Mead simplex method in low dimensions

Eötvös Loránd University Faculty of Informatics Budapest, Hungary

Acta Universitatis Sapientiae, Mathematica

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

{"article-title":"A hyperbolic variant of the Nelder\u2013Mead simplex method in low dimensions"}

The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically...

A hyperbolic variant of the Nelder–Mead simplex method in low dimensions

Published Online: Jun 06, 2014

Page range: 169 - 183

Received: Sep 04, 2013

DOI: https://doi.org/10.2478/ausm-2014-0012

© 2014

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.