Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older Gradient Descent and Adaptive Regularization Methods in Banach
  Spaces for First-Order Points   This paper considers optimization of smooth nonconvex functionals in smooth
infinite dimensional spaces. A H\"older gradient descent algorithm is first
proposed for finding approximate first-order points of regularized polynomial
functionals. This method is then applied to analyze the evaluation complexity
of an adaptive regularization method which searches for approximate first-order
points of functionals with $\beta$-H\"older continuous derivatives. It is shown
that finding an $\epsilon$-approximate first-order point requires at most
$O(\epsilon^{-\frac{p+\beta}{p+\beta-1}})$ evaluations of the functional and
its first $p$ derivatives.

6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn