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math.OC2022★ 2 cited
Graph and distributed extensions of the Douglas-Rachford method
Kristian Bredies, Enis Chenchene, Emanuele Naldi
In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of maximal monoto…
math.OC2021
Degenerate Preconditioned Proximal Point algorithms
Kristian Bredies, Enis Chenchene, Dirk A. Lorenz +1
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild…
math.OC2021
Weak topology and Opial property in Wasserstein spaces, with applications to Gradient Flows and Proximal Point Algorithms of geodesically convex functionals
Emanuele Naldi, Giuseppe Savaré
In this paper we discuss how to define an appropriate notion of weak topology in the Wasserstein space of Borel probability measures with finite quadratic…