Limited-memory BFGS

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Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the collection of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS) using a limited amount of computer memory. It is a popular algorithm for parameter estimation in machine learning. The algorithm's target problem is to minimize f ( x ) {\displaystyle f(\mathbf {x} )} over unconstrained values of the real-vector x {\displaystyle \mathbf {x} } where f {\displaystyle f} is a differentiable scalar function. Like the original BFGS, L-BFGS uses an estimate of the inverse Hessian matrix to steer its search through variable space, but where BFGS stores a dense n × n {\displaystyle n\times n} approximation to the inverse Hessian...

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