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 239 articles , 1 standard article )

Showing results 1 to 20 of 239.
Sorted by year (citations)

1 2 3 ... 10 11 12 next

  1. Ban, Jaepil; Seo, Minseok; Goh, Taedong; Jeong, Hyeyun; Kim, Sang Woo: Improved co-design of event-triggered dynamic output feedback controllers for linear systems (2020)
  2. Lai, Zhengshou; Chen, Qiushi; Huang, Linchong: Fourier series-based discrete element method for computational mechanics of irregular-shaped particles (2020)
  3. Lei, J.; Liu, Q. B.; Wang, X. Y.: Ensemble learning-based computational imaging method for electrical capacitance tomography (2020)
  4. Pöttinger, Markus; Ramlau, Ronny; Auzinger, Günter: A new temporal control approach for SCAO systems (2020)
  5. Vila, Roberto; Ferreira, Letícia; Saulo, Helton; Prataviera, Fábio; Ortega, Edwin: A bimodal gamma distribution: properties, regression model and applications (2020)
  6. Albrecht, Gudrun; Caliò, Franca; Miglio, Edie: Geometrically constrained surface (re)construction (2019)
  7. Aretz-Nellesen, Nicole; Grepl, Martin A.; Veroy, Karen: 3D-VAR for parameterized partial differential equations: a certified reduced basis approach (2019)
  8. Carbajo, Jesus; Prieto, Andrés; Ramis, J.; Río-Martín, Laura: A non-parametric fluid-equivalent approach for the acoustic characterization of rigid porous materials (2019)
  9. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Tomov, Vladimir: The target-matrix optimization paradigm for high-order meshes (2019)
  10. 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)
  11. Fajfar, Iztok; Bűrmen, Árpád; Puhan, Janez: The Nelder-Mead simplex algorithm with perturbed centroid for high-dimensional function optimization (2019)
  12. Fusek, M.; Michálek, J.: Statistical inference for type I multiply left-censored samples from Weibull distribution (2019)
  13. Gomes, Susana N.; Stuart, Andrew M.; Wolfram, Marie-Therese: Parameter estimation for macroscopic pedestrian dynamics models from microscopic data (2019)
  14. Holloway, C. R.; Smith, D. J.; Dyson, R. J.: Linear Rayleigh-Bénard stability of a transversely isotropic fluid (2019)
  15. Imakura, Akira: Minimal residual-like condition with collinearity for shifted Krylov subspace methods (2019)
  16. Li, Dongmin; Hu, Qingpei; Wang, Lujia; Yu, Dan: Statistical inference for (M_t/G/ Infinity) queueing systems under incomplete observations (2019)
  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)

1 2 3 ... 10 11 12 next