Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Douglas-Rachford and Peaceman-Rachford algorithms in the presence
  of uniform monotonicity and the absence of minimizers   The Douglas-Rachford and Peaceman-Rachford algorithms have been successfully
employed to solve convex optimization problems, or more generally finding zeros
of monotone inclusions. Recently, the behaviour of these methods in the
inconsistent case, i.e., in the absence of solutions has triggered significant
consideration. It has been shown that under mild assumptions the shadow
sequence of the Douglas-Rachford algorithm converges weakly to a generalized
solution when the underlying operators are subdifferentials of proper lower
semicontinuous convex functions. However, no convergence behaviour has been
proved in the case of Peaceman-Rachford algorithm. In this paper, we prove the
convergence of the shadow sequences associated with the Douglas-Rachford
algorithm and Peaceman-Rachford algorithm when one of the operators is
uniformly monotone and $3^*$ monotone but not necessarily a subdifferential.
Several examples illustrate and strengthen our conclusion.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph