The Douglas--Rachford Algorithm Converges Only Weakly
Minh N. Bùi, Patrick L. Combettes · SIAM Journal on Control and Optimization · 2020
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.