Existence, duality, and cyclical monotonicity for weak transport costs
By Julio D. Backhoff Veraguas, Mathias Beiglboeck, Gudmund Pammer. Calculus of Variations and Partial Differential Equations, 2018
104 citations recorded by the source corpus.
The optimal weak transport problem has recently been introduced by Gozlan et al. (J Funct Anal 273(11):3327–3405, 2017). We provide general existence and duality results for these problems on arbitrary Polish spaces, as well as a necessary and sufficient optimality criterion in the spirit of cyclical monotonicity. As an application we extend the Brenier–Strassen Theorem of Gozlan and Juillet (On a mixture of brenier and strassen theorems. arXiv:1808.02681, 2018) to general probability measures on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^d$$\end{document} under minimal assumptions. A driving idea behind our proofs is to consider the set of transport plans with a new (‘adapted’) topology which seems better suited for the weak transport problem and allows to carry out arguments which are close to the proofs in the classical setup.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/e4c1c61f9f131d597fbaed9f234d5618fd144456
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In Applied Mathematics
- Daniel Bartl
- Mathias Beiglbock
- Julio Backhoff-Veraguas
- Martin Huesmann
- Gudmund Pammer
- Sigrid Kallblad
- Manu Eder
- Johannes Wiesel
Citations in the corpus
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