Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iteration complexity of an inexact Douglas-Rachford method and of a
  Douglas-Rachford-Tseng's F-B four-operator splitting method for solving
  monotone inclusions   In this paper, we propose and study the iteration complexity of an inexact
Douglas-Rachford splitting (DRS) method and a Douglas-Rachford-Tseng's
forward-backward (F-B) splitting method for solving two-operator and
four-operator monotone inclusions, respectively. The former method (although
based on a slightly different mechanism of iteration) is motivated by the
recent work of J. Eckstein and W. Yao, in which an inexact DRS method is
derived from a special instance of the hybrid proximal extragradient (HPE)
method of Solodov and Svaiter, while the latter one combines the proposed
inexact DRS method (used as an outer iteration) with a Tseng's F-B splitting
type method (used as an inner iteration) for solving the corresponding
subproblems. We prove iteration complexity bounds for both algorithms in the
pointwise (non-ergodic) as well as in the ergodic sense by showing that they
admit two different iterations: one that can be embedded into the HPE method,
for which the iteration complexity is known since the work of Monteiro and
Svaiter, and another one which demands a separate analysis. Finally, we perform
simple numerical experiments %on three-operator and four-operator monotone
inclusions to show the performance of the proposed methods when compared with
other existing algorithms.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: bayes-an