Implementing the Nelder-Mead simplex algorithm with adaptive parameters

In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimen...

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Veröffentlicht in:Computational optimization and applications Jg. 51; H. 1; S. 259 - 277
Hauptverfasser: Gao, Fuchang, Han, Lixing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.01.2012
Springer Nature B.V
Schlagworte:
Adaptive algorithms
Algorithms
Computation
Convex and Discrete Geometry
Descent
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Parameter optimization
Simplex method
Statistics
Studies
Simplex
Polytope
Adaptive parameter
Nelder-Mead method
Optimization
ISSN:0926-6003, 1573-2894
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Zusammenfassung:In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the expansion, contraction, and shrink parameters depend on the dimension of the optimization problem. Our numerical experiments show that the new implementation outperforms the standard Nelder-Mead method for high dimensional problems.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-010-9329-3