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The Douglas--Rachford algorithm for normal cones converges only weakly
Abstract
We show that the Douglas--Rachford algorithm applied to two normal cone operators associated with closed convex sets can fail to converge strongly, even when one set is a closed vector subspace, the other is a closed convex cone, and their intersection is a singleton.
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BibTeX
@misc{bui2026douglasrachford,
title = {{The Douglas--Rachford algorithm for normal cones converges only weakly}},
author = {Minh N. Bùi and Honglin Luo and Xianfu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26147},
eprint = {2610.26147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26147},
}
RIS
TY - UNPB
TI - The Douglas--Rachford algorithm for normal cones converges only weakly
AU - Minh N. Bùi
AU - Honglin Luo
AU - Xianfu Wang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26147
UR - https://arxiv.org/abs/2610.26147
AB - We show that the Douglas--Rachford algorithm applied to two normal cone operators associated with closed convex sets can fail to converge strongly, even when one set is a closed vector subspace, the other is a closed convex cone, and their intersection is a singleton.
ER -