# Forward-backward truncated Newton methods for convex composite optimization

Patrinos, Panagiotis and Stella, Lorenzo and Bemporad, Alberto Forward-backward truncated Newton methods for convex composite optimization. Working Paper # /2014 ArXiv (Unpublished)

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## Abstract

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.

Item Type: Working Paper (Working Paper) A preliminary version of this paper [1] was presented at the 52nd IEEE Conference on Decision and Control, Florence, Italy, December 11, 2013. Q Science > QA Mathematics > QA75 Electronic computers. Computer science Computer Science and Applications Ms T. Iannizzi 01 Jul 2014 11:02 01 Jul 2014 11:02 http://eprints.imtlucca.it/id/eprint/2225