  We propose an algorithmic framework for convex minimization problems of a
composite function with two terms: a self-concordant function and a possibly
nonsmooth regularization term. Our method is a new proximal Newton algorithm
that features a local quadratic convergence rate. As a specific instance of our
framework, we consider the sparse inverse covariance matrix estimation in graph
learning problems. Via a careful dual formulation and a novel analytic
step-size selection procedure, our approach for graph learning avoids Cholesky
decompositions and matrix inversions in its iteration making it attractive for
parallel and distributed implementations.
