Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method

  title={Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method},
  author={Nikita Doikov and Y. Nesterov},
  journal={J. Optim. Theory Appl.},
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
15 Citations
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Stochastic Newton and Cubic Newton Methods with Simple Local Linear-Quadratic Rates
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Optimal Combination of Tensor Optimization Methods
Smoothness Parameter of Power of Euclidean Norm
Affine-invariant contracting-point methods for Convex Optimization
Stochastic Subspace Cubic Newton Method
Optimization Methods for Fully Composite Problems
Inexact Tensor Methods with Dynamic Accuracies


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