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...

Full description

Saved in:
Bibliographic Details
Published inComputational optimization and applications Vol. 51; no. 1; pp. 259 - 277
Main Authors Gao, Fuchang, Han, Lixing
Format Journal Article
LanguageEnglish
Published Boston Springer US 2012
Springer Nature B.V
Subjects
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
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-010-9329-3