About: Broyden–Fletcher–Goldfarb

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In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so by gradually improving an approximation to the Hessian matrix of the loss function, obtained only from gradient evaluations (or approximate gradient evaluations) via a generalized secant method.

Attributes	Values
rdf:type	software
rdfs:label	Broyden–Fletcher–Goldfarb–Shanno algorithm (en)
rdfs:comment	In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so by gradually improving an approximation to the Hessian matrix of the loss function, obtained only from gradient evaluations (or approximate gradient evaluations) via a generalized secant method. (en)
sameAs	Broyden–Fletcher–Goldfarb–Shanno algorithm
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Div_col dbt:Div_col_end dbt:More_citations_needed dbt:Redirect dbt:Reflist dbt:Short_description dbt:Optimization_algorithms
Subject	Optimization algorithms and methods
Link from a Wikipage to an external page	https://archive.org/details/practicalmethods0000flet
gold:hypernym	Method
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Broyden–Fletcher–Goldfarb–Shanno_algorithm?oldid=1021885250&ns=0
Wikipage page ID	1926409 (xsd:integer)
page length (characters) of wiki page	15273 (xsd:nonNegativeInteger)
Wikipage revision ID	1021885250 (xsd:integer)
Link from a Wikipage to another Wikipage	Nonlinear programming Numerical analysis Wiley (publisher) Artelys Knitro Berndt–Hall–Hall–Hausman algorithm Optimization algorithms and methods David Shanno Davidon–Fletcher–Powell formula Donald Goldfarb Positive definiteness Quasi-Newton method Secant method Wolfe conditions Charles George Broyden Credible interval Line search Preconditioner Sherman–Morrison formula Springer Science+Business Media Computational complexity of mathematical operations Confidence interval Hessian matrix Newton's method in optimization Optimization Toolbox GNU Scientific Library Gradient Gradient descent SciPy Symmetric rank-one Descent direction Invertible matrix Iterative method Loss function Pattern search (optimization) Levenberg–Marquardt algorithm Limited-memory BFGS Mathematical optimization Maximum likelihood estimation Nelder–Mead method R (programming language) Roger Fletcher (mathematician)
has abstract	In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so by gradually improving an approximation to the Hessian matrix of the loss function, obtained only from gradient evaluations (or approximate gradient evaluations) via a generalized secant method. Since the updates of the BFGS curvature matrix do not require matrix inversion, its computational complexity is only , compared to in Newton's method. Also in common use is L-BFGS, which is a limited-memory version of BFGS that is particularly suited to problems with very large numbers of variables (e.g., >1000). The BFGS-B variant handles simple box constraints. The algorithm is named after Charles George Broyden, Roger Fletcher, Donald Goldfarb and David Shanno. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Broyden–Fletcher–Goldfarb–Shanno_algorithm
is Wikipage redirect of	BFGS BFGS method Broyden-Fletcher-Goldfarb-Shanno algorithm Broydon-Fletcher-Goldfarb-Shanno
is Link from a Wikipage to another Wikipage of	Nonlinear conjugate gradient method Bayesian optimization Berndt–Hall–Hall–Hausman algorithm Broyden's method CASTEP CMA-ES Centroidal Voronoi tessellation David Shanno Davidon–Fletcher–Powell formula Donald Goldfarb Charles George Broyden Cholesky decomposition K-transform List of numerical analysis topics Hessian matrix List of algorithms Michael J. S. Dewar GHK algorithm Gauss–Newton algorithm Goldfarb Gradient descent IPOPT BFGS BFGS method Limited-memory BFGS Mathematical optimization Mathematics of artificial neural networks Maximum likelihood estimation Nelder–Mead method Broyden-Fletcher-Goldfarb-Shanno algorithm Broydon-Fletcher-Goldfarb-Shanno
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Broyden–Fletcher–Goldfarb–Shanno_algorithm

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