About: Backtracking line search

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In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction. Its use requires that the objective function is differentiable and that its gradient is known. Backtracking line search is typically used for gradient descent (GD), but it can also be used in other contexts. For example, it can be used with Newton's method if the Hessian matrix is positive definite.

Attributes	Values
rdf:type	software
rdfs:label	Backtracking line search (en)
rdfs:comment	In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction. Its use requires that the objective function is differentiable and that its gradient is known. Backtracking line search is typically used for gradient descent (GD), but it can also be used in other contexts. For example, it can be used with Newton's method if the Hessian matrix is positive definite. (en)
dcterms:subject	Optimization algorithms and methods Mathematical optimization
Wikipage page ID	1670188 (xsd:integer)
Wikipage revision ID	1098949890 (xsd:integer)
Link from a Wikipage to another Wikipage	Definite symmetric matrix Annals of Mathematical Statistics Riemann sum Deep learning Descent direction Compact space Critical point (mathematics) Analytic function Mathematical optimization Saddle point Norm (mathematics) Operator norm Wolfe conditions Gradient Gradient descent Morse theory Convex function Objective function Level set Limit (mathematics) Lipschitz continuity Subsequence Physical Review Letters Mathematical Programming Optimization algorithms and methods Learning rate Lebesgue measure Line search Expected value Normal distribution Stochastic gradient descent Invertible matrix Mathematical optimization Hessian matrix Differentiable function Dot product Society for Industrial and Applied Mathematics Integral NeurIPS Newton's method in optimization Athena Scientific Łojasiewicz inequality SIAM Journal on Optimization Springer-Verlag Step size dbr:Proceedings_of_Machine_Learning_Research
Link from a Wikipage to an external page	http://papers.neurips.cc/paper/8875-first-order-methods-almost-always-avoid-saddle-points-the-case-of-vanishing-step-sizes.pdf http://proceedings.mlr.press/v49/lee16.html https://drops.dagstuhl.de/opus/volltexte/2017/8164/pdf/LIPIcs-ITCS-2017-2.pdf https://books.google.com/books%3Fid=epc5fX0lqRIC http://projecteuclid.org/euclid.pjm/1102995080 https://dl.acm.org/doi/10.5555/2969033.2969154 https://projecteuclid.org/euclid.aoms/1177729586%7C http://www.athenasc.com/nonlinbook.html
sameAs	Backtracking line search Backtracking line search Backtracking line search
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Cite_book dbt:Cite_conference dbt:Cite_journal dbt:Fraction dbt:Harvtxt dbt:No_footnotes dbt:Short_description
has abstract	In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction. Its use requires that the objective function is differentiable and that its gradient is known. The method involves starting with a relatively large estimate of the step size for movement along the line search direction, and iteratively shrinking the step size (i.e., "backtracking") until a decrease of the objective function is observed that adequately corresponds to the amount of decrease that is expected, based on the step size and the local gradient of the objective function. The stopping criterion is known as the Armijo–Goldstein condition. Backtracking line search is typically used for gradient descent (GD), but it can also be used in other contexts. For example, it can be used with Newton's method if the Hessian matrix is positive definite. (en)
gold:hypernym	Method
prov:wasDerivedFrom	wikipedia-en:Backtracking_line_search?oldid=1098949890&ns=0
page length (characters) of wiki page	36986 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Backtracking_line_search
is rdfs:seeAlso of	Line search
is Link from a Wikipage to another Wikipage of	Limited-memory BFGS List of numerical analysis topics Gauss–Newton algorithm Wolfe conditions Gradient descent Line search Stochastic gradient descent Newton's method in optimization Backtracking linesearch Armijo-Goldstein condition Armijo-Goldstein rule Armijo condition Armijo rule Armijo–Goldstein condition Armijo–Goldstein rule
is Wikipage redirect of	Backtracking linesearch Armijo-Goldstein condition Armijo-Goldstein rule Armijo condition Armijo rule Armijo–Goldstein condition

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