fminsearch

Convergence properties of the Nelder--Mead simplex method in low dimensions 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 results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder--Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder--Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.


References in zbMATH (referenced in 267 articles , 1 standard article )

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  2. Aretz-Nellesen, Nicole; Grepl, Martin A.; Veroy, Karen: 3D-VAR for parameterized partial differential equations: a certified reduced basis approach (2019)
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  7. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Tomov, Vladimir: The target-matrix optimization paradigm for high-order meshes (2019)
  8. Dong, Jiaqi; Chen, Weiqi; Zeng, Zhe; Qin, Qing-Hua; Xiao, Yi: Analysis of wave band gaps in mechanical metamaterial based on Nelder-Mead method (2019)
  9. Fajfar, Iztok; Bűrmen, Árpád; Puhan, Janez: The Nelder-Mead simplex algorithm with perturbed centroid for high-dimensional function optimization (2019)
  10. Ferreiro, Ana M.; García-Rodríguez, José Antonio; Vázquez, Carlos; Costa e Silva, E.; Correia, A.: Parallel two-phase methods for global optimization on GPU (2019)
  11. Fusek, M.; Michálek, J.: Statistical inference for type I multiply left-censored samples from Weibull distribution (2019)
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  17. Morais, J. V.; Custódio, A. L.; Marques, G. M.: Calibration of parameters in dynamic energy budget models using direct-search methods (2019)
  18. Nguyen, Nhu; Yvonnet, J.; Réthoré, J.; Tran, A. B.: Identification of fracture models based on phase field for crack propagation in heterogeneous lattices in a context of non-separated scales (2019)
  19. Riaz, Bilal; Shuang, Cong; Qamar, Shahid: Optimal control methods for quantum gate preparation: a comparative study (2019)
  20. Stojsavljevic, Thomas; Pinter, Gabriella; Lauko, Istvan; Myers, Nicholas: Parameter identification and sensitivity analysis for a phytoplankton competition model (2019)

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