On the optimal parameter values of the Nelder–Mead simplex algorithm

Bürmen, Arpad (author), Puhan, Janez (author)

The paper outlines the derivation of optimal parameter values for the Nelder–Mead simplex algorithm as a function of the optimization problem’s dimension. The derivation applies to a general, strictly convex quadratic objective function, under the assumption that the simplex’s centroid probability density function within the ellipsoid defined by the simplex’s worst vertex is independent of the centroid’s distance to the worst vertex. The derived dependences of the Nelder–Mead simplex algorithm parameters show similarities with the heuristic solutions proposed so far. The algorithm’s performance, relative to its default parameter settings, was tested on a quadratic function in 10, 20, 50, and 100 dimensions.

• Language: English
• Keywords: unconstrained optimization, Nelder-Mead simplex algorithm, high dimensions, strictly convex quadratic function, meta-optimization
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 18 str.
• Numbering: Vol. 484, [art. 117521
• PID: 20.500.12556/RUL-180949
• UDC: 004
• ISSN on article: 0377-0427
• DOI: 10.1016/j.cam.2026.117521
• COBISS.SI-ID: 272417283
• Publication date in RUL: 20.03.2026

Record is a part of a journal

• Title: Journal of computational and applied mathematics
• Shortened title: J. comput. appl. math.
• Publisher: Elsevier
• ISSN: 0377-0427
• COBISS.SI-ID: 27496960

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: neomejena optimizacija, Nelder-Meadov simpleksni postopek, mnogo dimenzionalni prostor, striktno konveksna kriterijska funkcija, meta-optimizacija

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0246
• Name: ICT4QoL - Informacijsko komunikacijske tehnologije za kakovostno življenje