Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Attouch-Th\'era duality revisited: paramonotonicity and operator
  splitting   The problem of finding the zeros of the sum of two maximally monotone
operators is of fundamental importance in optimization and variational
analysis. In this paper, we systematically study Attouch-Th\'era duality for
this problem. We provide new results related to Passty's parallel sum, to
Eckstein and Svaiter's extended solution set, and to Combettes' fixed point
description of the set of primal solutions. Furthermore, paramonotonicity is
revealed to be a key property because it allows for the recovery of all primal
solutions given just one arbitrary dual solution. As an application, we
generalize the best approximation results by Bauschke, Combettes and Luke [J.
Approx. Theory 141 (2006), 63-69] from normal cone operators to paramonotone
operators. Our results are illustrated through numerous examples.

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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio