Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Methods for Finding Approximate Stationary Points of Convex
  Functions   In this paper we consider the problem of finding $\epsilon$-approximate
stationary points of convex functions that are $p$-times differentiable with
$\nu$-H\"{o}lder continuous $p$th derivatives. We present tensor methods with
and without acceleration. Specifically, we show that the non-accelerated
schemes take at most $\mathcal{O}\left(\epsilon^{-1/(p+\nu-1)}\right)$
iterations to reduce the norm of the gradient of the objective below a given
$\epsilon\in (0,1)$. For accelerated tensor schemes we establish improved
complexity bounds of
$\mathcal{O}\left(\epsilon^{-(p+\nu)/[(p+\nu-1)(p+\nu+1)]}\right)$ and
$\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-1/(p+\nu)}\right)$, when the
H\"{o}lder parameter $\nu\in [0,1]$ is known. For the case in which $\nu$ is
unknown, we obtain a bound of
$\mathcal{O}\left(\epsilon^{-(p+1)/[(p+\nu-1)(p+2)]}\right)$ for a universal
accelerated scheme. Finally, we also obtain a lower complexity bound of
$\mathcal{O}\left(\epsilon^{-2/[3(p+\nu)-2]}\right)$ for finding
$\epsilon$-approximate stationary points using $p$-order tensor methods.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph