A Simplex Method for Function Minimization

J. A. Nelder; R. Mead · The Computer Journal · 1965

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J. A. Nelder; R. Mead

Publisher

The Computer Journal

Year

1965

Language

English

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A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n + 1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

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APA 7

Nelder, J. A. & Mead, R. (1965). A Simplex Method for Function Minimization. https://doi.org/10.1093/comjnl/7.4.308

MLA

Nelder, J. A, and R. Mead. "A Simplex Method for Function Minimization." 1965. https://doi.org/10.1093/comjnl/7.4.308.

Chicago

Nelder, J. A. and R. Mead. 1965. "A Simplex Method for Function Minimization.". https://doi.org/10.1093/comjnl/7.4.308.

Harvard

Nelder, J. A. and Mead, R. 1965, A Simplex Method for Function Minimization, The Computer Journal, available at: https://doi.org/10.1093/comjnl/7.4.308 [Accessed 7 Aug. 2026].

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Resource details

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Title: A Simplex Method for Function Minimization

Author / contributors: J. A. Nelder; R. Mead

Publisher: The Computer Journal

Publication year: 1965

Language: English

Subjects

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Hessian matrix; Simplex; Minification; Neighbourhood (mathematics); Vertex (graph theory); Simplex algorithm; Mathematics; Mathematical optimization; Function (biology); Computer science; Combinatorics; Algorithm