Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nearly optimal first-order methods for convex optimization under
  gradient norm measure: An adaptive regularization approach   In the development of first-order methods for smooth (resp., composite)
convex optimization problems, where smooth functions with Lipschitz continuous
gradients are minimized, the gradient (resp., gradient mapping) norm becomes a
fundamental optimality measure. Under this measure, a fixed iteration algorithm
with the optimal iteration complexity is known, while determining this number
of iteration to obtain a desired accuracy requires the prior knowledge of the
distance from the initial point to the optimal solution set. In this paper, we
report an adaptive regularization approach, which attains the nearly optimal
iteration complexity without knowing the distance to the optimal solution set.
To obtain further faster convergence adaptively, we secondly apply this
approach to construct a first-order method that is adaptive to the H\"olderian
error bound condition (or equivalently, the {\L}ojasiewicz gradient property),
which covers moderately wide classes of applications. The proposed method
attains nearly optimal iteration complexity with respect to the gradient
mapping norm.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc