Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method

@article{Doikov2021MinimizingUC,
  title={Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method},
  author={Nikita Doikov and Y. Nesterov},
  journal={J. Optim. Theory Appl.},
  year={2021},
  volume={189},
  pages={317-339}
}
In this paper we study the iteration complexity of Cubic Regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain degree and justify the linear rate of convergence in a nondegenerate case for the method with an adaptive estimate of the regularization parameter. The algorithm automatically achieves the best possible global complexity bound among different problem classes of… Expand
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