Gilding the Lily: A Variant of the Nelder-Mead Algorithm Based on Golden-Section Search

@article{Nazareth2002GildingTL,
  title={Gilding the Lily: A Variant of the Nelder-Mead Algorithm Based on Golden-Section Search},
  author={Larry Nazareth and Paul Tseng},
  journal={Comp. Opt. and Appl.},
  year={2002},
  volume={22},
  pages={133-144}
}
We propose a variant of the Nelder-Mead algorithm derived from a reinterpretation of univariate golden-section direct search. In the univariate case, convergence of the variant can be analyzed analogously to golden-section search. In the multivariate case, we modify the variant by replacing strict descent with fortiied descent and maintaining the interior angles of the simplex bounded away from zero. Convergence of the modiied variant can be analyzed by applying results for a fortiied-descent… CONTINUE READING
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