Weak optimal total variation transport problems and generalized Wasserstein barycenters
| Autor: | Chung, Nhan-Phu, Trinh, Thanh-Son |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we establish a Kantorovich duality for weak optimal total variation transport problems. As consequences, we recover a version of duality formula for partial optimal transports established by Caffarelli and McCann; and we also get another proof of Kantorovich-Rubinstein Theorem for generalized Wasserstein distance $\widetilde{W}_1^{a,b}$ proved before by Piccoli and Rossi. Then we apply our duality formula to study generalized Wasserstein barycenters. We show the existence of these barycenters for measures with compact supports. Finally, we prove the consistency of our barycenters. Comment: 28 pages. Title is changed, introduction is expanded and new references are added. This also supersedes arXiv:1904.12461, which will not be submitted for publication. We improved our duality formulas to weak optimal total variation transport problems instead of the previous optimal total variation transport ones. Section 3 is rewritten. We also added two new Corollaries 1.2 and 1.3 |
| Databáze: | arXiv |
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