Corpus ID: 146808603

Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method

@article{Doikov2019MinimizingUC,
  title={Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method},
  author={Nikita Doikov and Y. Nesterov},
  journal={arXiv: Optimization and Control},
  year={2019}
}
  • Nikita Doikov, Y. Nesterov
  • Published 2019
  • Mathematics
  • arXiv: Optimization and Control
  • 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… CONTINUE READING
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