About: Davidon–Fletcher–Powell formula

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The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition. It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix. Given a function , its gradient, and positive-definite Hessian matrix , the Taylor series is and the Taylor series of the gradient itself (secant equation) is used to update .

Attributes	Values
rdf:type	yago:WikicatOptimizationAlgorithmsAndMethods yago:Abstraction100002137 yago:Act100030358 yago:Activity100407535 yago:Algorithm105847438 yago:Event100029378 yago:Procedure101023820 yago:PsychologicalFeature100023100 yago:YagoPermanentlyLocatedEntity yago:Rule105846932
rdfs:label	Davidon–Fletcher–Powell formula (en) DFP法 (ja)
rdfs:comment	The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition. It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix. Given a function , its gradient, and positive-definite Hessian matrix , the Taylor series is and the Taylor series of the gradient itself (secant equation) is used to update . (en)
dct:subject	Optimization algorithms and methods
Wikipage page ID	11231265 (xsd:integer)
Wikipage revision ID	994242340 (xsd:integer)
Link from a Wikipage to another Wikipage	Limited-memory BFGS Nelder–Mead method Quasi-Newton method Gradient Optimization algorithms and methods William C. Davidon Duality (mathematics) Taylor series Hessian matrix Positive-definite matrix Michael J. D. Powell Broyden–Fletcher–Goldfarb–Shanno algorithm Newton's method Newton's method in optimization Secant method Roger Fletcher (mathematician) Symmetric rank-one
Link from a Wikipage to an external page	https://archive.org/details/practicalmethods0000flet https://archive.org/details/methodsforuncons0000kowa/page/45 https://digital.library.unt.edu/ark:/67531/metadc1021816/
sameAs	Davidon–Fletcher–Powell formula Davidon–Fletcher–Powell formula Davidon–Fletcher–Powell formula Davidon–Fletcher–Powell formula
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Reflist dbt:Optimization_algorithms
has abstract	The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition. It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix. Given a function , its gradient, and positive-definite Hessian matrix , the Taylor series is and the Taylor series of the gradient itself (secant equation) is used to update . The DFP formula finds a solution that is symmetric, positive-definite and closest to the current approximate value of : where and is a symmetric and positive-definite matrix. The corresponding update to the inverse Hessian approximation is given by is assumed to be positive-definite, and the vectors and must satisfy the curvature condition The DFP formula is quite effective, but it was soon superseded by the Broyden–Fletcher–Goldfarb–Shanno formula, which is its dual (interchanging the roles of y and s). (en)
prov:wasDerivedFrom	wikipedia-en:Davidon–Fletcher–Powell_formula?oldid=994242340&ns=0
page length (characters) of wiki page	3902 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Davidon–Fletcher–Powell_formula
is Link from a Wikipage to another Wikipage of	Non-linear least squares Davidon-Fletcher-Powell algorithm Charles George Broyden List of numerical analysis topics Maximum likelihood estimation Gauss–Newton algorithm Wolfe conditions Gradient descent 1968 North Indian Ocean cyclone season Davidon-Fletcher-Powell formula Davidson-Fletcher-Powell 1968 Burma cyclone Broyden's method William C. Davidon DFP updating formula Michael J. D. Powell Broyden–Fletcher–Goldfarb–Shanno algorithm Roger Fletcher (mathematician) Davidon-Fletcher-Powell Davidon–Fletcher–Powell Davidon–Fletcher–Powell algorithm
is Wikipage redirect of	Davidon-Fletcher-Powell algorithm Davidon-Fletcher-Powell formula Davidson-Fletcher-Powell DFP updating formula Davidon-Fletcher-Powell Davidon–Fletcher–Powell Davidon–Fletcher–Powell algorithm
is known for of	Michael J. D. Powell
is known for of	Michael J. D. Powell
is foaf:primaryTopic of	wikipedia-en:Davidon–Fletcher–Powell_formula

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