Quasi $α$-Firmly Nonexpansive Mappings in Wasserstein Spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929749113176064 |
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| author | Bërdëllima, Arian Steidl, Gabriele |
| author_facet | Bërdëllima, Arian Steidl, Gabriele |
| contents | This paper introduces the concept of quasi $α$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $α$-firmly nonexpansive mappings satisfying a certain quadratic growth condition, the fixed point iterations converge in the narrow topology. As a byproduct, we will get the known convergence of the proximal point algorithm in Wasserstein spaces. We apply our results to show for the first time that cyclic proximal point algorithms for minimizing the sum of certain functionals on Wasserstein spaces converge under appropriate assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_04851 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quasi $α$-Firmly Nonexpansive Mappings in Wasserstein Spaces Bërdëllima, Arian Steidl, Gabriele Functional Analysis Metric Geometry Probability 46T99, 47H10, 47J26, 28A33 This paper introduces the concept of quasi $α$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $α$-firmly nonexpansive mappings satisfying a certain quadratic growth condition, the fixed point iterations converge in the narrow topology. As a byproduct, we will get the known convergence of the proximal point algorithm in Wasserstein spaces. We apply our results to show for the first time that cyclic proximal point algorithms for minimizing the sum of certain functionals on Wasserstein spaces converge under appropriate assumptions. |
| title | Quasi $α$-Firmly Nonexpansive Mappings in Wasserstein Spaces |
| topic | Functional Analysis Metric Geometry Probability 46T99, 47H10, 47J26, 28A33 |
| url | https://arxiv.org/abs/2203.04851 |