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Cubic regularization of Newton method and its global performance. (English) Zbl 1142.90500
Summary: 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.

MSC:
90C53 Methods of quasi-Newton type
90C30 Nonlinear programming
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