Mathematical Programming

, Volume 108, Issue 1, pp 177–205 | Cite as

Cubic regularization of Newton method and its global performance

  • Yurii NesterovEmail author
  • B.T. Polyak


In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme, we prove general local convergence results. However, the main contribution of the paper is related to global worst-case complexity bounds for different problem classes including some nonconvex cases. It is shown that the search direction can be computed by standard linear algebra technique.


General nonlinear optimization Unconstrained optimization Newton method Trust-region methods Global complexity bounds Global rate of convergence 

Mathematics Subject Classification (1991)

49M15 49M37 58C15 90C25 90C30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Center for Operations Research and Econometrics (CORE)Catholic University of Louvain (UCL)Louvain-la-NeuveBelgium
  2. 2.Institute of Control ScienceMoscowRussia

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