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Updated: Sep 24, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
Published on: July 28, 2013
Local convergence of tensor methods
Nikita Doikov1, Yurii Nesterov2
1Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Catholic University of Louvain (UCL), Louvain-la-Neuve, 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 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.
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