Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Methods for Minimizing Convex Functions with H\"{o}lder
  Continuous Higher-Order Derivatives   In this paper we study $p$-order methods for unconstrained minimization of
convex functions that are $p$-times differentiable ($p\geq 2$) with
$\nu$-H\"{o}lder continuous $p$th derivatives. We propose tensor schemes with
and without acceleration. For the schemes without acceleration, we establish
iteration complexity bounds of
$\mathcal{O}\left(\epsilon^{-1/(p+\nu-1)}\right)$ for reducing the functional
residual below a given $\epsilon\in (0,1)$. Assuming that $\nu$ is known, we
obtain an improved complexity bound of
$\mathcal{O}\left(\epsilon^{-1/(p+\nu)}\right)$ for the corresponding
accelerated scheme. For the case in which $\nu$ is unknown, we present a
universal accelerated tensor scheme with iteration complexity of
$\mathcal{O}\left(\epsilon^{-p/[(p+1)(p+\nu-1)]}\right)$. A lower complexity
bound of $\mathcal{O}\left(\epsilon^{-2/[3(p+\nu)-2]}\right)$ is also obtained
for this problem class.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga