%0 Report
%9 Working Paper
%A Patrinos, Panagiotis
%A Stella, Lorenzo
%A Bemporad, Alberto
%D 2014
%F eprints:2225
%I IMT Institute for Advanced Studies Lucca
%N  
%T Forward-backward truncated Newton methods for convex composite optimization
%U http://eprints.imtlucca.it/2225/
%X 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. 
%Z A preliminary version of this paper [1] was presented at the 52nd IEEE Conference on Decision and Control, Florence, Italy, December 11, 2013.