A hyperbolic variant of the Nelder–Mead simplex method in low dimensions

[1] C. Barbu, L-I. Pi¸scoran, The orthopole theorem in the Poincar´e disc model of hyperbolic geometry, Acta Univ. Sapientiae Math., 4 (2012), 20-25.Search in Google Scholar

[2] S. Fridli, P. Kov´acs, L. L´ocsi, F. Schipp, Rational modeling of multi-lead QRS complexes in ECG signals, Ann. Univ. Sci. Budapest., Sect. Comput., 36 (2012), 145-155.Search in Google Scholar

[3] L. Han, M. Neumann, Effect of dimensionality on the Nelder-Mead simplex method, Optim. Methods Softw., 21 (2006), 1-16.10.1080/10556780512331318290Search in Google Scholar

[4] L. Han, M. Neumann, J. Xu, On the roots of certain polynomials arising from the analysis of the Nelder-Mead simplex method, Linear Algebra Appl., 363 (2003), 109-124.10.1016/S0024-3795(02)00485-8Search in Google Scholar

[5] J. C. Lagarias, J. A. Reeds, M. H.Wright, P. E.Wright, Convergence properties of the Nelder-Mead algorithm in low dimensions, SIAM J. Optim., 9 (1998), 112-147.10.1137/S1052623496303470Search in Google Scholar

[6] J. C. Lagarias, B. Poonen, M. H. Wright, Convergence of the restricted Nelder-Mead algorithm in two dimensions, SIAM J. Optim., 22 (2012), 501-532.10.1137/110830150Search in Google Scholar

[7] L. L´ocsi, Approximating poles of complex rational functions, Acta Univ. Sapientiae Math., 1 (2009), 169-182.Search in Google Scholar

[8] L. L´ocsi, Investigating hyperbolic variants of the Nelder-Mead simplex method, Abstracts of the J´anos Bolyai Memorial Conference, (2010), 49.Search in Google Scholar

[9] K. I. M. McKinnon, Convergence of the Nelder-Mead simplex method to a non-stationary point, SIAM J. Optim., 9 (1998), 148-158.10.1137/S1052623496303482Search in Google Scholar

[10] J. A. Nelder, R. Mead, A simplex method for function minimization, Comput. J., 7 (1965), 308-313.10.1093/comjnl/7.4.308Search in Google Scholar

[11] C. J. Price, I. D. Coope, D. Byatt, A convergent variant of the Nelder- Mead algorithm, J. Optim. Theory App., 113 (2002), 5-19.10.1023/A:1014849028575Search in Google Scholar

[12] M. H. Wright, Nelder, Mead, and the other simplex method, Doc. Math., Extra Volume: Optimization Stories (2012), 271-276. Search in Google Scholar