L-BFGS is an algorithm for quasi-Newton optimization. L-BFGS uses the Broyden–Fletcher–Goldfarb–Shanno update to approximate the Hessian matrix (L-BFGS stands for 'limited memory BFGS'). L-BFGS is particularly well suited for optimization problems with a large number of dimensions. This is because L-BFGS never explicitly forms or stores the Hessian matrix, which can be quite expensive when the number of dimensions <math>n\,\!</math> becomes large.

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  • L-BFGS is an algorithm for quasi-Newton optimization. L-BFGS uses the Broyden–Fletcher–Goldfarb–Shanno update to approximate the Hessian matrix (L-BFGS stands for 'limited memory BFGS'). L-BFGS is particularly well suited for optimization problems with a large number of dimensions. This is because L-BFGS never explicitly forms or stores the Hessian matrix, which can be quite expensive when the number of dimensions <math>n\,\!</math> becomes large. Instead, L-BFGS maintains a history of the past <math>m\,\!</math> updates of the position <math>x\,\!</math> and gradient <math>\nabla f(x)</math>, where generally the history <math>m\,\!</math> can be short, often less than 10. These updates are used to implicitly do operations requiring the Hessian (or its inverse). While strictly, a straight-forward BFGS implementation at the <math>i\,\!</math>th iteration would represent the Hessian approximation as informed by all updates on <math>0 \ldots i-1</math>, L-BFGS does quite well using updates from only the most recent iterations <math>i-m \ldots i-1</math>.
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  • L-BFGS is an algorithm for quasi-Newton optimization. L-BFGS uses the Broyden–Fletcher–Goldfarb–Shanno update to approximate the Hessian matrix (L-BFGS stands for 'limited memory BFGS'). L-BFGS is particularly well suited for optimization problems with a large number of dimensions. This is because L-BFGS never explicitly forms or stores the Hessian matrix, which can be quite expensive when the number of dimensions <math>n\,\!</math> becomes large.
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  • L-BFGS
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