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 271 articles , 1 standard article )

Showing results 61 to 80 of 271.
Sorted by year (citations)

previous 1 2 3 4 5 6 ... 12 13 14 next

  1. Kong, Dehan; Ibrahim, Joseph G.; Lee, Eunjee; Zhu, Hongtu: FLCRM: functional linear Cox regression model (2018)
  2. Lukassen, Axel Ariaan; Kiehl, Martin: Parameter estimation with model order reduction for elliptic differential equations (2018)
  3. Matthes, Jörg; Waibel, Patrick; Keller, Hubert B.; Gröll, Lutz: Identification and control of the waelz process using infrared image processing (2018)
  4. Piotrowski, Adam P.: Across neighborhood search algorithm: a comprehensive analysis (2018)
  5. Sai, Aditya; Kong, Nan: Characterising model dynamics using sparse grid interpolation: parameter estimation of cholera (2018)
  6. Tuncer, Necibe; Le, Trang T.: Structural and practical identifiability analysis of outbreak models (2018)
  7. Weron, Aleksander: Mathematical models for dynamics of molecular processes in living biological cells a single particle tracking approach (2018)
  8. Abbiati, Roberto Andrea; Cagnardi, Petra; Ravasio, Giuliano; Villa, Roberto; Manca, Davide: A physiologically based model for tramadol pharmacokinetics in horses (2017)
  9. Alibert, Jean-Jacques; Della Corte, Alessandro; Giorgio, Ivan; Battista, Antonio: Extensional \textitElasticain large deformation as (\Gamma)-limit of a discrete 1D mechanical system (2017)
  10. Alkhalifa, Loay; Brimberg, Jack: Locating a minisum annulus: a new partial coverage distance model (2017)
  11. Auer, Ekaterina; Senkel, Luise; Kiel, Stefan; Rauh, Andreas: Control-oriented models for SO fuel cells from the angle of V&V: analysis, simplification possibilities, performance (2017)
  12. Boujo, E.; Noiray, N.: Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation (2017)
  13. de Abreu Corrêa, Lucio; Quezada, Juan Carlos; Cottereau, Régis; d’Aguiar, Sofia Costa; Voivret, Charles: Randomly-fluctuating heterogeneous continuum model of a ballasted railway track (2017)
  14. Doltsinis, Ioannis: Plastic limit of structures and energy principles (2017)
  15. Kazeykina, Anna; Klein, Christian: Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation (2017)
  16. Li, Zhiming; Teng, Zhidong; Miao, Hui: Modeling and control for HIV/AIDS transmission in China based on data from 2004 to 2016 (2017)
  17. Matsui, Kota; Kumagai, Wataru; Kanamori, Takafumi: Parallel distributed block coordinate descent methods based on pairwise comparison oracle (2017)
  18. Steponavičė, Ingrida; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: Dynamic algorithm selection for Pareto optimal set approximation (2017)
  19. Sträng, Jan Eric; Schuler, Rainer; Kühl, Michael; Kestler, Hans A.: Switch-like behavior enables Wnt11 concentration specific response during dorso-ventral axis formation in \textitXenopuslaevis (2017)
  20. Tarkhamtham, Payap; Sirisrisakulchai, Jirakom; Tansuchat, Roengchai: Portfolio optimization of energy commodity futures returns with minimum information copula (2017)

previous 1 2 3 4 5 6 ... 12 13 14 next