The Nelder-Mead Component

6/11/2009

Updated 27/04/2010

In this page, we present the main features of the Nelder-Mead component in Scilab, starting from v5.2. The goal of this page is to be an introduction to Scilab's Nelder-Mead User Manual, which is provided at the end of this document.

The goal of this component is to provide a Nelder-Mead direct search optimization method. That Nelder-Mead algorithm may be used in the following optimization context :

This component has been proposed in SEP #21: SEP_21_neldermead.odt.

On this base, Scilab now provides the function "fminsearch", which is able to reproduce Matlab's fminsearch.

Overview

The following is a list of features the Nelder-Mead prototype algorithm currently provides :

Nelder-Mead User's Manual

In this section, we present the Nelder-Mead User's Manual.

Abstract

In this document, we present the Nelder-Mead component provided in Scilab. The introduction gives a brief overview of the optimization features of the component and present an introductory example. Then we present some theory associated with the simplex, a geometric concept which is central in the Nelder-Mead algorithm. We present several method to compute an initial simplex. Then we present Spendley's et al. fixed shape unconstrained optimization algorithm. Several numerical experiments are provided, which shows how this algorithm performs on well-scaled and badly scaled quadratics. In the final section, we present the Nelder-Mead variable shape unconstrained optimization algorithm. Several numerical experiments are presented, where some of these are counter examples, that is cases where the algorithms fails to converge on a stationnary point. In the appendix of this document, the interested reader will find a bibliography of simplex-based algorithms, along with an analysis of the various implementations which are available in several programming languages.

The User's Manual is a 130 pages document provided in pdf format.

This document is maintained in the Scilab forge at :

http://forge.scilab.org/index.php/p/docneldermead/

The latest pdf version is available at :

http://forge.scilab.org/index.php/p/docneldermead/downloads/

The LaTeX source is provided under the terms of the Creative Commons Attribution-ShareAlike 3.0 Unported License :

http://creativecommons.org/licenses/by-sa/3.0/

public: The Nelder-Mead Component (last edited 2011-12-08 11:21:38 by favignana)