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Cubic regularization of a Newton scheme and its global performance

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Nesterov, Yurii [UCL] Polyak, Boris

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.

Document type Document de travail (Working Paper)
Access type Accès libre
Publication date 2003
Collection CORE Discussion Papers - 2003/41
Affiliation UCL - CORE - Center for Operations Research and Econometrics
Keywords General nonlinear optimization ; Unconstrained optimization ; Newton method ; Trust-region methods ; Global complexity bounds ; Global rate of convergence
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Bibliographic reference Nesterov, Yurii ; Polyak, Boris. Cubic regularization of a Newton scheme and its global performance. CORE Discussion Papers ; 2003/41 (2003)
Permanent URL http://hdl.handle.net/2078.1/4920