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\subsection{The Algorithms}  The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm \cite{Liu_Nocedal_1989} is employed for solving high-dimensional minimization problems in scenarios where both the objective function and its gradient can be computed analytically. The L-BFGS algorithm belongs to the class of quasi-Newton optimization routines, which solve the given minimization problem by computing approximations to the Hessian matrix of the objective function.  Trying out the math: