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.
|Titolo:||Proximal newton methods for convex composite optimization|
|Data di pubblicazione:||2013|
|Appare nelle tipologie:||4.1 Contributo in Atti di convegno|