Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear convergence of inexact descent method and inexact proximal
  gradient algorithms for lower-order regularization problems   The $\ell_p$ regularization problem with $0< p< 1$ has been widely studied
for finding sparse solutions of linear inverse problems and gained successful
applications in various mathematics and applied science fields. The proximal
gradient algorithm is one of the most popular algorithms for solving the
$\ell_p$ regularisation problem. In the present paper, we investigate the
linear convergence issue of one inexact descent method and two inexact proximal
gradient algorithms (PGA). For this purpose, an optimality condition theorem is
explored to provide the equivalences among a local minimum, second-order
optimality condition and second-order growth property of the $\ell_p$
regularization problem. By virtue of the second-order optimality condition and
second-order growth property, we establish the linear convergence properties of
the inexact descent method and inexact PGAs under some simple assumptions. Both
linear convergence to a local minimal value and linear convergence to a local
minimum are provided. Finally, the linear convergence results of the inexact
numerical methods are extended to the infinite-dimensional Hilbert spaces.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph