# On Inexact Solution of Auxiliary Problems in Tensor Methods for Convex Optimization

arXiv: https://arxiv.org/abs/1907.13023 · HTML: https://mlsanity.com/paper/1907.13023/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Super-Universal Regularized Newton Method](https://mlsanity.com/paper/2208.05888/) (2022)
- [Perseus: A Simple and Optimal High-Order Method for Variational Inequalities](https://mlsanity.com/paper/2205.03202/) (2022)
- [Gradient-Normalized Smoothness for Optimization with Approximate Hessians](https://mlsanity.com/paper/2506.13710/) (2025)

## Abstract (arXiv)

In this paper we study the auxiliary problems that appear in p-order tensor methods for unconstrained minimization of convex functions with nu-H"older continuous pth derivatives. This type of auxiliary problems corresponds to the minimization of a (p+nu)-order regularization of the pth order Taylor approximation of the objective. For the case p=3, we consider the use of Gradient Methods with Bregman distance. When the regularization parameter is sufficiently large, we prove that the referred methods take at most O(log(ε-1)) iterations to find either a suitable approximate stationary point of the tensor model or an ε-approximate stationary point of the original objective function.