Broyden–Fletcher–Goldfarb–Shanno algorithm (Q2877013)

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optimization method

• BFGS algorithm

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Language	Label	Description	Also known as
English	Broyden–Fletcher–Goldfarb–Shanno algorithm	optimization method	BFGS algorithm

Statements

instance of

algorithm

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subclass of

Quasi-Newton method

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part of

nonlinear programming

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named after

Charles George Broyden

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Roger Fletcher

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Donald Goldfarb

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David Shanno

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discoverer or inventor

Charles George Broyden

point in time

1970

1 reference

DOI

10.1093/IMAMAT/6.1.76

Roger Fletcher

point in time

1970

1 reference

DOI

10.1093/COMJNL/13.3.317

Donald Goldfarb

point in time

1970

1 reference

stated in

A family of variable-metric methods derived by variational means

David Shanno

point in time

1970

1 reference

DOI

10.1090/S0025-5718-1970-0274029-X

defining formula

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

1 reference

stated in

Numerical Optimization

computes solution to

optimization problem

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

BabelNet ID

17280119n

1 reference

stated in

BabelNet

Freebase ID

/m/066pcg

1 reference

stated in

Freebase Data Dumps

publication date

28 October 2013

Microsoft Academic ID

132721684

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OpenAlex ID

C132721684

1 reference

stated in

OpenAlex

retrieved

26 January 2022

reference URL

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

 

Sitelinks

Wikipedia(8 entries)

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• 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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