Cubic regularization of a Newton scheme and its global performance

Yurii Nesterov and Boris Polyak

No 2003041, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper we suggest a cubic regularization for a Newton method as applied to unconstrained minimization problem. For this scheme we prove general convergence results. We analyze the behavior of this scheme on different problem classes, for which we get global and local worst-case complexity bounds. It is shown that the search direction can be computed by a standard linear algebra technique.

Keywords: general nonlinear optimization; unconstrained optimization; Newton method; trust-region methods; global complexity bounds; global rate of convergence (search for similar items in EconPapers)
Date: 2003-05
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Citations: View citations in EconPapers (3)

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