A Stochastic Convergence Result for the Nelder-Mead Simplex Method

被引：6
作者：
Galantai, Aurel [1 ]
机构：
[1] Obuda Univ, H-1034 Budapest, Hungary
来源：
MATHEMATICS | 2023年 / 11卷 / 09期
关键词：
Nelder-Mead simplex method; convergence; stochastic convergence; ALGORITHM;
D O I：
10.3390/math11091998
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the Nelder-Mead simplex method converges in the sense that the simplex vertices converge to a common limit point with a probability of one. The result may explain the practical usefulness of the Nelder-Mead method.
引用
收藏
页数：12
相关论文
共 22 条
[1]  
[Anonymous], 2002, Nonhomogeneous matrix products
[2]  
Audet C., 2017, Springer Series in Operations Research and Financial Engineering
[3]  
Borovkov A.A., 2013, Probability Theory
[4]  
CHANDRA T. K., 2012, SpringerBriefs Stat., DOI [10.1007/978-81-322-0677-4, DOI 10.1007/978-81-322-0677-4]
[5]  
Conn AR, 2009, MOS-SIAM SER OPTIMIZ, V8, P1
[6]  
Galántai A, 2021, ACTA POLYTECH HUNG, V18, P93
[7]   Convergence of the Nelder-Mead method [J].
Galantai, Aurel .
NUMERICAL ALGORITHMS, 2022, 90 (03) :1043-1072
[8]  
Galntai A., 2020, J. Comput. Appl. Mech, V15, P115, DOI [10.32973/jcam.2020.008, DOI 10.32973/JCAM.2020.008]
[9]   Effect of dimensionality on the Nelder-Mead simplex method [J].
Han, LX ;
Neumann, M .
OPTIMIZATION METHODS & SOFTWARE, 2006, 21 (01) :1-16
[10]  
Kelley C. T., 1999, Iterative Methods for Optimization
123