Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Linear Convergence of the Approximate Proximal Splitting Method
  for Non-Smooth Convex Optimization   Consider the problem of minimizing the sum of two convex functions, one being
smooth and the other non-smooth. In this paper, we introduce a general class of
approximate proximal splitting (APS) methods for solving such minimization
problems. Methods in the APS class include many well-known algorithms such as
the proximal splitting method (PSM), the block coordinate descent method (BCD)
and the approximate gradient projection methods for smooth convex optimization.
We establish the linear convergence of APS methods under a local error bound
assumption. Since the latter is known to hold for compressive sensing and
sparse group LASSO problems, our analysis implies the linear convergence of the
BCD method for these problems without strong convexity assumption.

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The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph