(Q2877013)

English

Broyden–Fletcher–Goldfarb–Shanno algorithm

optimization method

BFGS algorithm

In more languages

Statements

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Quasi-Newton method

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nonlinear programming

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Charles George Broyden

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Donald Goldfarb

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discoverer or inventor

Charles George Broyden

1970

1 reference

10.1093/IMAMAT/6.1.76

1970

1 reference

10.1093/COMJNL/13.3.317

Donald Goldfarb

1970

1 reference

A family of variable-metric methods derived by variational means

1970

1 reference

10.1090/S0025-5718-1970-0274029-X

defining formula

{\begin{aligned}{\bf {p_{k}}}&=-B_{k}^{-1}\nabla {\bf {f_{k}}}\\\alpha _{k}&=\arg \min f({\bf {x_{k}+\alpha {\bf {p_{k})}}}}\\{\bf {s_{k}}}&=\alpha _{k}{\bf {p_{k}}}\\{\bf {x_{k+1}}}&={\bf {x_{k}+{\bf {s_{k}}}}}\\{\bf {y_{k+1}}}&=\nabla {\bf {f_{k+1}-\nabla {\bf {f_{k}}}}}\\B_{k+1}&=B_{k}+{\frac {\bf {y_{k}{\bf {y_{k}^{\top }}}}}{\bf {y_{k}^{\top }{\bf {s_{k}}}}}}-{\frac {B_{k}{\bf {s}}_{k}{\bf {s}}_{k}^{\top }B_{k}^{\top }}{{\bf {s}}_{k}^{\top }B_{k}{\bf {s}}_{k}}}\end{aligned}}

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Numerical Optimization

computes solution to

optimization problem

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

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Freebase Data Dumps

publication date

28 October 2013

Microsoft Academic ID

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

Sitelinks

Wikipedia(8 entries)

dewiki BFGS-Verfahren
enwiki Broyden–Fletcher–Goldfarb–Shanno algorithm
fawiki روش بی‌اف‌جی‌اس
frwiki Méthode de Broyden-Fletcher-Goldfarb-Shanno
jawiki BFGS法
ruwiki Алгоритм Бройдена — Флетчера — Гольдфарба — Шанно
ukwiki Алгоритм Бройдена — Флетчера — Гольдфарба — Шанно
zhwiki BFGS算法

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