Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coordinate Descent Methods for Fractional Minimization   We consider a class of structured fractional minimization problems, in which
the numerator part of the objective is the sum of a differentiable convex
function and a convex nonsmooth function, while the denominator part is a
concave or convex function. This problem is difficult to solve since it is
nonconvex. By exploiting the structure of the problem, we propose two
Coordinate Descent (CD) methods for solving this problem. One is applied to the
original fractional function, the other is based on the associated parametric
problem. The proposed methods iteratively solve a one-dimensional subproblem
\textit{globally}, and they are guaranteed to converge to coordinate-wise
stationary points. In the case of a convex denominator, we prove that the
proposed CD methods using sequential nonconvex approximation find stronger
stationary points than existing methods. Under suitable conditions, CD methods
with an appropriate initialization converge linearly to the optimal point (also
the coordinate-wise stationary point). In the case of a concave denominator, we
show that the resulting problem is quasi-convex, and any critical point is a
global minimum. We prove that the algorithms converge to the global optimal
solution with a sublinear convergence rate. We demonstrate the applicability of
the proposed methods to some machine learning and signal processing models. Our
experiments on real-world data have shown that our method significantly and
consistently outperforms existing methods in terms of accuracy.

32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat