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 271 articles , 1 standard article )

Showing results 241 to 260 of 271.
Sorted by year (citations)

previous 1 2 3 ... 11 12 13 14 next

  1. Rahman, M. K.: An intelligent moving object optimization algorithm for design problems with mixed variables, mixed constraints and multiple objectives (2006)
  2. Stemp, Peter J.; Herbert, Ric D: Solving non-linear models with saddle-path instabilities (2006)
  3. Baranoski, Gladimir V. G.; Krishnaswamy, Aravind; Kimmel, Bradley: Increasing the predictability of tissue subsurface scattering simulations (2005) ioport
  4. Jaranowski, Piotr; Królak, Andrzej: Gravitational-wave data analysis. Formalism and sample applications: the Gaussian Case (2005)
  5. Rolland-Lagan, Anne-Gaëlle; Coen, Enrico; Impey, Stephen J.; Bangham, J. Andrew: A computational method for inferring growth parameters and shape changes during development based on clonal analysis (2005)
  6. Sontag, Laura; Axelrod, David E.: Evaluation of pathways for progression of heterogeneous breast tumors (2005)
  7. Barlow, Martin; Gusev, Yuri; Lai, Manpo: Calibration of multifactor models in electricity markets (2004)
  8. Barrowes, Benjamin E.; O’Neill, Kevin; Grzegorczyk, Tomasz M.; Kong, Jin A.: On the asymptotic expansion of the spheroidal wave function and its eigenvalues for complex size parameter (2004)
  9. Bartz-Beielstein, T.; Parsopoulos, K. E.; Vrahatis, M. N.: Design and analysis of optimization algorithms using computational statistics (2004)
  10. Mawardi, A.; Pitchumani, R.: Cure cycle design for thermosetting-matrix composites fabrication under uncertainty (2004)
  11. Østby, Ivar; Winther, Ragnar: Stability of a model of human granulopoiesis using continuous maturation (2004)
  12. Vartiainen, Juha J.; Niskanen, Antti O.; Nakahara, Mikio; Salomaa, Martti M.: Acceleration of quantum algorithms using three-qubit gates (2004)
  13. Gilli, M.; Winker, P.: A global optimization heuristic for estimating agent based models (2003)
  14. He, Li; Kárný, Miroslav: Estimation and prediction with ARMMAX model: A mixture of ARMAX models with common ARX part (2003)
  15. Kolda, Tamara G.; Lewis, Robert Michael; Torczon, Virginia: Optimization by direct search: New perspectives on some Classical and modern methods (2003)
  16. Nazareth, John Lawrence: Differentiable optimization and equation solving. A treatise on algorithmic science and the Karmarkar revolution (2003)
  17. Alvarez-Vázquez, L. J.; Martínez, A.; Rodríguez, C.; Vázquez-Méndez, M. E.: Numerical optimization for the location of wastewater outfalls (2002)
  18. Banks, H. T.; Barnes, J. H.; Eberhardt, A.; Tran, H.; Wynne, S.: Modeling and computation of propagating waves from coronary stenoses (2002)
  19. García-Palomares, U. M.; Rodríguez, J. F.: New sequential and parallel derivative-free algorithms for unconstrained minimization (2002)
  20. Nazareth, Larry; Tseng, Paul: Gilding the lily: A variant of the Nelder-Mead algorithm based on Golden-section search (2002)

previous 1 2 3 ... 11 12 13 14 next