Convergence of the Nelder-Mead method

DOI10.1007/s11075-021-01221-7zbMath1495.65089OpenAlexW3212793018MaRDI QIDQ2672718

Aurel Galantai

Publication date: 13 June 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-021-01221-7

zbMATH Keywords

convergence analysisNelder-Mead simplex methodderivative-free minimization

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Derivative-free methods and methods using generalized derivatives (90C56)

Uses Software

• KELLEY
• fminsearch

Cites Work

• Characterization and properties of matrices with \(k\)-involutory symmetries
• On matrix norms and logarithmic norms
• The boundedness of all products of a pair of matrices is undecidable
• Direct search methods: Then and now
• On the roots of certain polynomials arising from the analysis of the Nelder-Mead simplex method
• Nelder, Mead, and the other simplex method
• Infinite powers of matrices and characteristic roots
• Convergence of the Restricted Nelder--Mead Algorithm in Two Dimensions
• Effect of dimensionality on the Nelder–Mead simplex method
• Introduction to Derivative-Free Optimization
• Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
• Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point
• Infinite products and paracontracting matrices
• Derivative-Free and Blackbox Optimization
• Deeper Inside PageRank
• Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition
• A Simplex Method for Function Minimization
• Convergence theorems for the Nelder-Mead method
• Using the Borsuk-Ulam theorem. Lectures on topological methods in combinatorics and geometry. Written in cooperation with Anders Björner and Günter M. Ziegler
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