Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse
  regression   This paper conducts a comparative study of proximal gradient methods (PGMs)
and proximal DC algorithms (PDCAs) for sparse regression problems which can be
cast as Difference-of-two-Convex-functions (DC) optimization problems. It has
been shown that for DC optimization problems, both General Iterative Shrinkage
and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge
to critical points. Recently some enhanced versions of PDCAs are shown to
converge to d-stationary points, which are stronger necessary condition for
local optimality than critical points. In this paper we claim that without any
modification, PGMs converge to a d-stationary point not only to DC problems but
also to more general nonsmooth nonconvex problems under some technical
assumptions. While the convergence to d-stationary points is known for the case
where the step size is small enough, the finding of this paper is valid also
for extended versions such as GIST and its alternating optimization version,
which is to be developed in this paper. Numerical results show that among
several algorithms in the two categories, modified versions of PGM perform best
among those not only in solution quality but also in computation time.

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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: stat