Cubic regularization of Newton method and its global performance |
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Authors: | Yurii Nesterov BT Polyak |
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Institution: | (1) Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium;(2) Institute of Control Science, Profsojuznaya 65, Moscow, 117997, Russia |
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Abstract: | 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. |
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Keywords: | General nonlinear optimization Unconstrained optimization Newton method Trust-region methods Global complexity bounds Global rate of convergence |
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