?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F2225%2F&rft.title=Forward-backward+truncated+Newton+methods+for+convex+composite+optimization&rft.creator=Patrinos%2C+Panagiotis&rft.creator=Stella%2C+Lorenzo&rft.creator=Bemporad%2C+Alberto&rft.subject=QA75+Electronic+computers.+Computer+science&rft.description=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%2C+namely+the+forward-backward+envelope+(FBE).+The+first+algorithm+is+based+on+a+standard+line+search+strategy%2C+whereas+the+second+one+combines+the+global+efficiency+estimates+of+the+corresponding+first-order+methods%2C+while+achieving+fast+asymptotic+convergence+rates.+Furthermore%2C+they+are+computationally+attractive+since+each+Newton+iteration+requires+the+approximate+solution+of+a+linear+system+of+usually+small+dimension.+&rft.publisher=ArXiv&rft.date=2014&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Patrinos%2C+Panagiotis+and+Stella%2C+Lorenzo+and+Bemporad%2C+Alberto++Forward-backward+truncated+Newton+methods+for+convex+composite+optimization.++Working+Paper++%23+%2F2014++++ArXiv+++++++(Unpublished)+++&rft.relation=http%3A%2F%2Farxiv.org%2Fabs%2F1402.6655