Implementing the Nelder-Mead simplex algorithm with adaptive parameters

@article{Gao2012ImplementingTN,
  title={Implementing the Nelder-Mead simplex algorithm with adaptive parameters},
  author={F. Gao and Lixing Han},
  journal={Computational Optimization and Applications},
  year={2012},
  volume={51},
  pages={259-277}
}
  • F. Gao, Lixing Han
  • Published 2012
  • Computer Science, Mathematics
  • Computational Optimization and Applications
  • In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the expansion, contraction, and shrink parameters depend on the dimension of the optimization problem. Our numerical… CONTINUE READING

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