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arXiv · 1402.6655

Forward-backward truncated Newton methods for convex composite optimization

Panagiotis Patrinos·Lorenzo Stella·Alberto Bemporad
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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.

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Panagiotis Patrinos, Lorenzo Stella, Alberto Bemporad. 2014-02-26. Forward-backward truncated Newton methods for convex composite optimization. https://arxiv.org/abs/1402.6655

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