Optimization on Microcomputers: The Nelder-Mead Simplex Algorithm

Dennis, J. E.; Woods, Daniel John

doi:10.21236/ada453814

Cited by 56 publications

(52 citation statements)

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“…In addition to examining different parameter values across a grid, the optimum parameters with respect to C 3 (θ) are estimated using the Nelder Meade simplex search algorithm [21,9]. Note that the topologies generated by the topology generators are random in a statistical sense, due to differing random seeds for each run.…”

Section: Resultsmentioning

confidence: 99%

Tuning Topology Generators Using Spectral Distributions

Haddadi

Fay

Uhlig

et al. 2008

Performance Evaluation: Metrics, Models and Benchmarks

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Abstract. An increasing number of synthetic topology generators are available, each claiming to produce representative Internet topologies. Every generator has its own parameters, allowing the user to generate topologies with different characteristics. However, there exist no clear guidelines on tuning the value of these parameters in order to obtain a topology with specific characteristics.In this paper we optimize the parameters of several topology generators to match a given Internet topology. The optimization is performed either with respect to the link density, or to the spectrum of the normalized Laplacian matrix. Contrary to approaches in the literature that rely only on the largest eigenvalues, we take into account the set of all eigenvalues. However, we show that on their own the eigenvalues cannot be used to construct a metric for optimizing parameters. Instead we present a weighted spectral method which simultaneously takes into account all the properties of the graph.

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Section: Resultsmentioning

confidence: 99%

Tuning Topology Generators Using Spectral Distributions

Haddadi

Fay

Uhlig

et al. 2008

Performance Evaluation: Metrics, Models and Benchmarks

View full text Add to dashboard Cite

show abstract

“…There is no guarantee that a descent direction will exist in the nonsmooth case, as the next example shows. Consider the following variant of the Dennis-Woods function [94]:…”

Section: The Effects Of Multiple Search Directions and Samplingmentioning

confidence: 99%

“…This function is continuous and strictly convex, but its gradient is discontinuous everywhere on the line x 1 = x 2 . In [94], it was shown that a modification of the Nelder-Mead simplex algorithm can fail to converge to the minimizer of f . Now consider a point of the form (a, a) T , with a = 0.…”

Section: The Effects Of Multiple Search Directions and Samplingmentioning

confidence: 99%

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

2003

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Abstract. Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.

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“…The Nelder-Mead simplex direct search algorithm implemented in MAT-LAB's fminsearch and described in New Computing Environments: Microcomputers in Large-Scale Computing (Dennis and Woods, 1987), goes through k iterations. It begins by sampling n + 1 time values, which we will refer to as x 1 , x 2 , · · · , x n+1 .…”

Section: The Nelder-mead Simplex Direct Searchmentioning

confidence: 99%

A Comparison and Catalog of Intrinsic Tumor Growth Models

2014

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Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global least squares minimization algorithm based on a combination of Nelder-Mead simplex direct search and Monte Carlo Markov Chain methods.

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Optimization on Microcomputers: The Nelder-Mead Simplex Algorithm

Cited by 56 publications

References 0 publications

Tuning Topology Generators Using Spectral Distributions

Tuning Topology Generators Using Spectral Distributions

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

A Comparison and Catalog of Intrinsic Tumor Growth Models

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