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Broyden–Fletcher–Goldfarb–Shanno algorithm

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…

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Overview

Numerical Numerical analysis
Optimization Optimization (mathematics)
Iterative method
Nonlinear optimization
Davidon–Fletcher–Powell method Davidon–Fletcher–Powell formula
Descent direction
Preconditioning Preconditioned gradient descent
Gradient
Hessian matrix
Loss function
Secant method
Matrix inversion
Computational complexity Computational complexity of mathematical operations
Newton's method Newton's method in optimization
L-BFGS
Compact representation Compact quasi-Newton representation
Charles George Broyden
Roger Fletcher Roger Fletcher (mathematician)
Donald Goldfarb
David Shanno

Rationale

Line search
Strongly convex Strongly convex function
Wolfe conditions
Symmetric rank-one
Positive definiteness

Algorithm

Twice-differentiable Smoothness
Gradient descent
Sherman–Morrison formula
Maximum likelihood Maximum likelihood estimation
Credible intervals Credible interval
Confidence intervals Confidence interval
Inverse Matrix inverse

Notable implementations

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Broyden–Fletcher–Goldfarb–Shanno algorithm

Nodes49

Edges48

Triples1

Avg. degree1.96

Density0.040816

Components1

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Important terminology

displaystyle mathbf bfgs matrix search algorithm optimization line alpha hessian function method also problems gradient update direction fletcher l-bfgs nabla

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Subject	Predicate	Object	Confidence	Src
B k	instance of	using an expansion	0.80	text

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