@incollection{eprints2226, month = {December}, publisher = {IEEE}, pages = {2358--2363}, author = {Panagiotis Patrinos and Alberto Bemporad}, booktitle = {52nd IEEE Conference on Decision and Control}, title = {Proximal Newton methods for convex composite optimization}, year = {2013}, keywords = {Approximation algorithms, Approximation methods, Convergence, Gradient methods, Radio frequency, Signal processing algorithms}, abstract = {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.}, url = {http://eprints.imtlucca.it/2226/} }