Forward-backward truncated Newton methods for convex composite optimization
Optimization and Control
2014-03-03 v2
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.
Cite
@article{arxiv.1402.6655,
title = {Forward-backward truncated Newton methods for convex composite optimization},
author = {Panagiotis Patrinos and Lorenzo Stella and Alberto Bemporad},
journal= {arXiv preprint arXiv:1402.6655},
year = {2014}
}