Implementable tensor methods in unconstrained convex optimization

@article{Nesterov2021ImplementableTM,
  title={Implementable tensor methods in unconstrained convex optimization},
  author={Y. Nesterov},
  journal={Mathematical Programming},
  year={2021},
  volume={186},
  pages={157 - 183}
}
  • Y. Nesterov
  • Published 2021
  • Mathematics, Computer Science, Medicine
  • Mathematical Programming
In this paper we develop new tensor methods for unconstrained convex optimization, which solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial. We analyze the simplest scheme, based on minimization of a regularized local model of the objective function, and its accelerated version obtained in the framework of estimating sequences. Their rates of convergence are compared with the worst-case lower complexity bounds for corresponding problem classes. Finally… Expand
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