L-BFGS (Low-memory Broyden–Fletcher–Goldfarb–Shanno) is a library for doing estimation and application of Hessians in numerical optimization while using limited memory and never explicitly creating the Hessian. Only simple vector operation are used, as specified by the L-BFGS algorithm.

The specific L-BFGS algorithm implemented here can be found in Algorithm 9.1 (L-BFGS two-loop recursion).

Moreover, the condition for the Cautious-BFGS (C-BFGS) algorithm, specified in D.-H. Li and M. Fukushima, "On the global convergence of the BFGS method for nonconvex unconstrained optimization problems", is used to check the updates of the L-BFGS.

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