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 )

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  1. Morais, J. V.; Custódio, A. L.; Marques, G. M.: Calibration of parameters in dynamic energy budget models using direct-search methods (2019)
  2. 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)
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  5. Uhlig, Frank: The construction of high order convergent look-ahead finite difference formulas for Zhang neural networks (2019)
  6. Wessing, Simon: Proper initialization is crucial for the Nelder-Mead simplex search (2019)
  7. Yang, Kaifeng; Emmerich, Michael; Deutz, André; Bäck, Thomas: Efficient computation of expected hypervolume improvement using box decomposition algorithms (2019)
  8. Ahi, Emrah; Akgiray, Vedat; Sener, Emrah: Robust term structure estimation in developed and emerging markets (2018)
  9. Ahookhosh, Masoud; Neumaier, Arnold: Solving structured nonsmooth convex optimization with complexity (\mathcalO(\varepsilon^-1/2)) (2018)
  10. Audet, Charles; Tribes, Christophe: Mesh-based Nelder-Mead algorithm for inequality constrained optimization (2018)
  11. Ban, Jaepil; Kwon, Wookyong; Won, Sangchul; Kim, Sangwoo: Robust (H_\infty) finite-time control for discrete-time polytopic uncertain switched linear systems (2018)
  12. Boem, Francesca; Zhou, Yilun; Fischione, Carlo; Parisini, Thomas: Distributed Pareto-optimal state estimation using sensor networks (2018)
  13. Bouclier, Robin; Passieux, Jean-Charles: A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis (2018)
  14. Chagas, T. P.; Bliman, P.-A.; Kienitz, K. H.: Stabilization of periodic orbits of discrete-time dynamical systems using the prediction-based control: new control law and practical aspects (2018)
  15. Chelle, Pierre; Morin, Claire; Montmartin, Aurélie; Piot, Michèle; Cournil, Michel; Tardy-Poncet, Brigitte: Evaluation and calibration of in silico models of thrombin generation using experimental data from healthy and haemophilic subjects (2018)
  16. Dong, Fanghu; Yin, Guosheng: Maximum likelihood estimation for incomplete multinomial data via the weaver algorithm (2018)
  17. Gómez-Tostón, Carolina; Barrena, Manuel; Cortés, Álvaro: Characterizing the optimal pivots for efficient similarity searches in vector space databases with Minkowski distances (2018)
  18. Gonçalves-E-Silva, Kayo; Aloise, Daniel; Xavier-De-Souza, Samuel; Mladenović, Nenad: Less is more: simplified Nelder-Mead method for large unconstrained optimization (2018)
  19. Hermanns, M.; Cramer, E.: Inference with progressively censored (k)-out-of-(n) system lifetime data (2018)
  20. Kheybari, S.; Darvishi, M. T.: An efficient technique to find semi-analytical solutions for higher order multi-point boundary value problems (2018)

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