# Tensor Methods for Minimizing Convex Functions with H"older Continuous Higher-Order Derivatives

arXiv: https://arxiv.org/abs/1904.12559 · HTML: https://mlsanity.com/paper/1904.12559/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2019.

## Built on by (most cited first, 4 of 4)

- [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)
- [Primal Acceleration of Newton's Method](https://mlsanity.com/paper/2608.21359/) (2026)

## Abstract (arXiv)

In this paper we study p-order methods for unconstrained minimization of convex functions that are p-times differentiable (p≥ 2) with nu-H"older continuous pth derivatives. We propose tensor schemes with and without acceleration. For the schemes without acceleration, we establish iteration complexity bounds of Oleft(ε-1/(p+nu-1)right) for reducing the functional residual below a given ε∈ (0,1). Assuming that nu is known, we obtain an improved complexity bound of Oleft(ε-1/(p+nu)right) for the corresponding accelerated scheme. For the case in which nu is unknown, we present a universal accelerated tensor scheme with iteration complexity of Oleft(ε-p/[(p+1)(p+nu-1)]right). A lower complexity bound of Oleft(ε-2/[3(p+nu)-2]right) is also obtained for this problem class.