4 citations · 13 across the 15 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…
Regression models for compositional data: General log-contrast formulations, proximal optimization, and microbiome data applications
Patrick L. Combettes, Christian L. Müller
Compositional data sets are ubiquitous in science, including geology, ecology, and microbiology. In microbiome research, compositional data primarily arise from high-throughput seq…
Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators
Patrick L. Combettes, Jean-Christophe Pesquet
Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants…