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Local convergence of tensor methods

Author

Listed:
  • DOIKOV Nikita,

    (Université catholique de Louvain, CORE, Belgium)

  • NESTEROV Yurii,

    (Université catholique de Louvain, CORE, Belgium)

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 higher-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 metods can be globalized using the inexact proximal iterations.

Suggested Citation

  • DOIKOV Nikita, & NESTEROV Yurii,, 2019. "Local convergence of tensor methods," LIDAM Discussion Papers CORE 2019021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2019021
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