Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions

  title={Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions},
  author={Jeffrey C. Lagarias and James A. Reeds and Margaret H. Wright and Paul E. Wright},
  journal={SIAM Journal on Optimization},
The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper presents convergence properties of the Nelder–Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence… CONTINUE READING
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