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Forward-backward truncated Newton methods for convex composite optimization

Panagiotis Patrinos(panagiotis.patrinos***at***imtlucca.it)
Lorenzo Stella(lorenzo.stella***at***imtlucca.it)
Alberto Bemporad(alberto.bemporad***at***imtlucca.it)

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.

Keywords: Convex composite optimization, Nonsmooth optimization, Operator splitting methods, Proximal algorithms, Newton methods, Conjugate gradient

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

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Entry Submitted: 02/27/2014
Entry Accepted: 02/27/2014
Entry Last Modified: 02/27/2014

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