Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Douglas-Rachford algorithm   The Douglas-Rachford algorithm is a very popular splitting technique for
finding a zero of the sum of two maximally monotone operators. However, the
behaviour of the algorithm remains mysterious in the general inconsistent case,
i.e., when the sum problem has no zeros. More than a decade ago, however, it
was shown that in the (possibly inconsistent) convex feasibility setting, the
shadow sequence remains bounded and it is weak cluster points solve a best
approximation problem.
  In this paper, we advance the understanding of the inconsistent case
significantly by providing a complete proof of the full weak convergence in the
convex feasibility setting. In fact, a more general sufficient condition for
the weak convergence in the general case is presented. Several examples
illustrate the results.

6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn