The Nelder Mead Component

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.

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