English

The Douglas--Rachford Algorithm Converges Only Weakly

Optimization and Control 2019-12-23 v1

Abstract

We show that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence. Likewise, we show that strong convergence can fail for the method of partial inverses.

Keywords

Cite

@article{arxiv.1912.09564,
  title  = {The Douglas--Rachford Algorithm Converges Only Weakly},
  author = {Minh N. Bùi and Patrick L. Combettes},
  journal= {arXiv preprint arXiv:1912.09564},
  year   = {2019}
}
R2 v1 2026-06-23T12:51:50.141Z