Local convergence of tensor methods

Doikov, Nikita;Nesterov, Yurii
(2022) Mathematical Programming — Vol. 193, n° 1, p. 315-336 (2022)

Files

CORE_RP_3239.pdf
  • Open Access
  • Adobe PDF
  • 681.93 KB
Download

Details

Authors
  • Doikov, Nikitaorcid-logoUCLouvain
    Author
  • Nesterov, Yuriiorcid-logoUCLouvain
    Author
Abstract
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also discussed. Lastly, we show how local convergence of the methods can be globalized using the inexact proximal iterations.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Doikov, N., & Nesterov, Y. (2022). Local convergence of tensor methods. Mathematical Programming, 193(1), 315-336. https://doi.org/10.1007/s10107-020-01606-x (Original work published 2022)