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\section{Introduction}  In this vignette we demonstrate how to use the \textbf{lbfgs} R package. \footnote{We are extremely thankful for the advice and support of Dustin Tingley.} The original motivation for writing the package was the lack of a general R implementation of the Orthant-Wise Quasi-Newton Limited-Memory (OWL-QN) optimization algorithm \cite{Andrew_Gao_2007}, except in limited-scope contexts. The package uses the libLBFGS C++ library written by Naoaki Okazaki (2010) (2010), which itself is a port of the Fortran method by Jorge Nocedal \cite{Nocedal_1980}.   \subsection{The Algorithms}  Trying out the math: