Local convergence of tensor methods

Nikita, Doikov () and Yurii, Nesterov ()
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Nikita, Doikov: Université catholique de Louvain, CORE, Belgium
Yurii, Nesterov: Université catholique de Louvain, CORE, Belgium

No 2019021, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: convex optimization; high-order methods; tensor methods; local convergence; uniform convexity; proximal methods (search for similar items in EconPapers)
Date: 2019-11-27
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