Cubic regularization of Newton method and its global performance

Nesterov, Yurii;Polyak, Boris
(2006) Mathematical Programming — Vol. 108, n° 1, p. 177-205 (2006)

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  • Nesterov, YuriiUCLouvain
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  • Polyak, Boris
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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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Nesterov, Y., & Polyak, B. (2006). Cubic regularization of Newton method and its global performance. Mathematical Programming, 108(1), 177-205. https://doi.org/10.1007/s10107-006-0706-8 (Original work published 2006)