Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The global rate of convergence for optimal tensor methods in smooth
  convex optimization   We consider convex optimization problems with the objective function having
Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new
tensor method, which closes the gap between the lower
$O\left(\varepsilon^{-\frac{2}{3p+1}} \right)$ and upper
$O\left(\varepsilon^{-\frac{1}{p+1}} \right)$ iteration complexity bounds for
this class of optimization problems.
  We also consider uniformly convex functions, and show how the proposed method
can be accelerated under this additional assumption. Moreover, we introduce a
$p$-th order condition number which naturally arises in the complexity analysis
of tensor methods under this assumption.
  Finally, we make a numerical study of the proposed optimal method and show
that in practice it is faster than the best known accelerated tensor method. We
also compare the performance of tensor methods for $p=2$ and $p=3$ and show
that the 3rd-order method is superior to the 2nd-order method in practice.

19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn