Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the local convergence of the Douglas-Rachford algorithm   We discuss the Douglas-Rachford algorithm to solve the feasibility problem
for two closed sets $A,B$ in $\mathbb{R}^d$. We prove its local convergence to
a fixed point when $A,B$ are finite unions of convex sets. We also show that
for more general nonconvex sets the scheme may fail to converge and start to
cycle, and may then even fail to solve the feasibility problem.

24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio