# Local convergence of tensor methods

arXiv: https://arxiv.org/abs/1912.02516 · HTML: https://mlsanity.com/paper/1912.02516/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [Super-Universal Regularized Newton Method](https://mlsanity.com/paper/2208.05888/) (2022)
- [Minimizing Quasi-Self-Concordant Functions by Gradient Regularization of Newton Method](https://mlsanity.com/paper/2308.14742/) (2023)
- [Perseus: A Simple and Optimal High-Order Method for Variational Inequalities](https://mlsanity.com/paper/2205.03202/) (2022)
- [Sketch-and-Project Meets Newton Method: Global mathcal O(k-2) Convergence with Low-Rank Updates](https://mlsanity.com/paper/2305.13082/) (2023)
- [Higher-Order Newton Methods with Polynomial Work per Iteration](https://mlsanity.com/paper/2311.06374/) (2023)
- [Second-Order Optimization with Asynchronous Curvature](https://mlsanity.com/paper/2510.15714/) (2025)

## Abstract (arXiv)

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.