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 approximation to the Hessian matrix of the loss function, obtained only from gradient evaluations (or approximate gradient evaluations) via a generalized secant method.
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- enIn 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.
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- enIn 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.
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- enBroyden–Fletcher–Goldfarb–Shanno algorithm
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- ALGLIB
- Artelys Knitro
- BHHH algorithm
- Category:Optimization algorithms and methods
- Charles George Broyden
- Computational complexity of mathematical operations
- Confidence interval
- Credible interval
- Davidon–Fletcher–Powell formula
- David Shanno
- Descent direction
- Donald Goldfarb
- GNU Octave
- GNU Scientific Library
- Gradient
- Gradient descent
- Hessian matrix
- Iterative method
- John Wiley & Sons
- Julia (programming language)
- L-BFGS
- Levenberg–Marquardt algorithm
- Line search
- Loss function
- Mathematica
- Matrix inverse
- Matrix inversion
- Maximum likelihood estimation
- Nelder–Mead method
- Newton's method in optimization
- Nonlinear optimization
- Numerical analysis
- Optimization (mathematics)
- Optimization Toolbox
- Pattern search (optimization)
- Positive definiteness
- Preconditioned gradient descent
- Quasi-Newton methods
- R (programming language)
- Roger Fletcher (mathematician)
- SciPy
- Secant method
- Sherman–Morrison formula
- Strongly convex function
- Symmetric rank-one
- Trust region
- Wolfe conditions
- SameAs
- 2fepT
- BFGS-Verfahren
- BFGS法
- BFGS算法
- m.066pcg
- Méthode de Broyden-Fletcher-Goldfarb-Shanno
- Q2877013
- Алгоритм Бройдена — Флетчера — Гольдфарба — Шанно
- Алгоритм Бройдена — Флетчера — Гольдфарба — Шанно
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- Category:Optimization algorithms and methods
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- Broyden–Fletcher–Goldfarb–Shanno algorithm?oldid=1124576811&ns=0
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- 1926409
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