Forward-backward truncated Newton methods for convex composite optimization

This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the second one combines the global efficiency estimates of the corresponding first-order methods, while achieving fast asymptotic convergence rates. Furthermore, they are computationally attractive since each Newton iteration requires the approximate solution of a linear system of usually small dimension

On the linear convergence of descent methods for convex essentially smooth minimization

Cover title.Includes bibliographical references (p. 27-31).Research supported by the U.S. Army Research Office. DAAL03-86-K-0171 Research supported by the National Science Foundation. NSF-DDM-8903385 Research supported by a grant from the Science and Engineering Research Board of McMaster University.by Zhi-Quan Luo, Paul Tseng