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math.OC2019
The Douglas--Rachford Algorithm Converges Only Weakly
Minh N. Bùi, Patrick L. Combettes
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. Lik…
math.OC2019
Warped Proximal Iterations for Monotone Inclusions
Minh N. Bùi, Patrick L. Combettes
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monot…
math.OC2019
Bregman Forward-Backward Operator Splitting
Minh N. Bùi, Patrick L. Combettes
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclid…