The Nelder-Mead Simplex Algorithm Is Sixty Years Old: New Convergence Results and Open Questions

被引:2
作者
Galantai, Aurel [1 ]
机构
[1] Obuda Univ, Software Engn Inst, John Von Neumann Fac Informat, H-1034 Budapest, Hungary
关键词
Nelder-Mead simplex methods; convergence; comparison; DERIVATIVE-FREE OPTIMIZATION; MATRICES; PRODUCTS;
D O I
10.3390/a17110523
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We investigate and compare two versions of the Nelder-Mead simplex algorithm for function minimization. Two types of convergence are studied: the convergence of function values at the simplex vertices and convergence of the simplex sequence. For the first type of convergence, we generalize the main result of Lagarias, Reeds, Wright and Wright (1998). For the second type of convergence, we also improve recent results which indicate that the Lagarias et al.'s version of the Nelder-Mead algorithm has better convergence properties than the original Nelder-Mead method. This paper concludes with some open questions.
引用
收藏
页数:21
相关论文
共 34 条
[1]  
[Anonymous], 2002, Nonhomogeneous matrix products
[2]  
Audet C., 2017, Derivative-free and Blackbox Optimization
[3]  
Barnett S., 1990, Games and Sets
[4]  
Beyn W.J., 1997, Electron. J. Linear Al, V2, P1, DOI [10.13001/1081-3810.1006, DOI 10.13001/1081-3810.1006]
[5]   The boundedness of all products of a pair of matrices is undecidable [J].
Blondel, VD ;
Tsitsiklis, JN .
SYSTEMS & CONTROL LETTERS, 2000, 41 (02) :135-140
[6]  
Conn AR, 2009, MOS-SIAM SER OPTIMIZ, V8, P1
[7]   SETS OF MATRICES ALL INFINITE PRODUCTS OF WHICH CONVERGE [J].
DAUBECHIES, I ;
LAGARIAS, JC .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 161 :227-263
[8]  
Galantai A, 2024, ACTA POLYTECH HUNG, V21, P185
[9]  
Galántai A, 2021, ACTA POLYTECH HUNG, V18, P93
[10]   A Stochastic Convergence Result for the Nelder-Mead Simplex Method [J].
Galantai, Aurel .
MATHEMATICS, 2023, 11 (09)