 Inexact accelerated high-order proximal-point methodsYurii, Nesterov ()
No 2020008, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Abstract: In this paper, we present a new framework of Bi-Level Unconstrained Minimization (BLUM) for development of accelerated methods in Convex Programming. These methods use approximations of the high-order proximal points, which are solutions of some auxiliary parametric optimization problems. For computing these points, we can use different methods, and, in particular, the lower-order schemes. This opens a possibility for the latter methods to overpass traditional limits of the Complexity Theory. As an example, we obtain a new second-order method with the convergence rate O(k^{-4}), where k is the iteration counter. This rate is better than the maximal possible rate of convergence for this type of methods, as applied to functions with Lipschitz continuous Hessian. We also present new methods with the exact auxiliary search procedure, which have the rate of convergence O(k^{−(3p+1)/2}), where p ≥ 1 is the order of the proximal operator. The auxiliary problem at each iteration of these schemes is convex. Keywords: convex optimization; tensor methods; proximal-point operator; lower complexity bounds; optimal methods (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2020008 Access Statistics for this paper More papers in LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.