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\subsection{The OWL-QN Algorithm}  The L-BFGS method cannot be applied to problems with an objective function of the form $r(x) = C \cdot \lvert \lvert x \lvert \lvert _1C  = \cdor C \cdot  \sum_i \lvert x_i \lvert$, such as LASSO regression or $L_1$-penalized log-linear models, given the non-differentiability of the objective function at any point where at least one of the parameters is zero. The OWL-QN algorithm exploits the fact that $L_1$-regularized objective functions will still