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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer-Verlag

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10.1007/bf02897104

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1436-4646

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Accelerating the cubic regularization of Newton’s

Authors: Yu Nesterov
Publish Date: 2007/01/20
Volume: 112, Issue: 1, Pages: 159-181
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Abstract

In this paper we propose an accelerated version of the cubic regularization of Newton’s method Nesterov and Polyak in Math Program 1081 177–205 2006 The original version used for minimizing a convex function with Lipschitzcontinuous Hessian guarantees a global rate of convergence of order Obig1 over k2big where k is the iteration counter Our modified version converges for the same problem class with order Obig1 over k3big keeping the complexity of each iteration unchanged We study the complexity of both schemes on different classes of convex problems In particular we argue that for the secondorder schemes the class of nondegenerate problems is different from the standard classThe research results presented in this paper have been supported by a grant “Action de recherche concertè ARC 04/09315” from the “Direction de la recherche scientifique Communautè française de Belgique” The scientific responsibility rests with the author

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