%0 Book Section
%A Patrinos, Panagiotis
%A Bemporad, Alberto
%B 52nd IEEE Conference on Decision and Control
%D 2013
%F eprints:2226
%I IEEE
%K Approximation algorithms, Approximation methods, Convergence, Gradient methods, Radio frequency, Signal processing algorithms
%P 2358-2363
%T Proximal Newton methods for convex composite optimization
%U http://eprints.imtlucca.it/2226/
%X This paper proposes two proximal Newton methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a new continuously differentiable exact penalty function, namely the Composite Moreau Envelope. 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 solution of a linear system of usually small dimension.