Weak topology and Opial property in Wasserstein spaces, with applications to gradient flows and proximal point algorithms of geodesically convex functionals

DOI10.4171/RLM/955zbMath1484.60002arXiv2104.06121MaRDI QIDQ2116067

Emanuele Naldi, Giuseppe Savaré

Publication date: 16 March 2022

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.06121

zbMATH Keywords

weak topologyoptimal transportgradient flowsdisplacement convexityWasserstein space

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Numerical optimization and variational techniques (65K10) Methods involving semicontinuity and convergence; relaxation (49J45) Optimal transportation (49Q22)

Cites Work

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• Monotone Operators and the Proximal Point Algorithm
• The Variational Formulation of the Fokker--Planck Equation
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Optimal Transport

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