Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iteration-Complexity of a Generalized Forward Backward Splitting
  Algorithm   In this paper, we analyze the iteration-complexity of Generalized
Forward--Backward (GFB) splitting algorithm, as proposed in \cite{gfb2011}, for
minimizing a large class of composite objectives $f + \sum_{i=1}^n h_i$ on a
Hilbert space, where $f$ has a Lipschitz-continuous gradient and the $h_i$'s
are simple (\ie their proximity operators are easy to compute). We derive
iteration-complexity bounds (pointwise and ergodic) for the inexact version of
GFB to obtain an approximate solution based on an easily verifiable termination
criterion. Along the way, we prove complexity bounds for relaxed and inexact
fixed point iterations built from composition of nonexpansive averaged
operators. These results apply more generally to GFB when used to find a zero
of a sum of $n > 0$ maximal monotone operators and a co-coercive operator on a
Hilbert space. The theoretical findings are exemplified with experiments on
video processing.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph